{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "02d7e531",
   "metadata": {
    "origin_pos": 0
   },
   "source": [
    "# 概率\n",
    ":label:`sec_prob`\n",
    "\n",
    "简单地说，机器学习就是做出预测。\n",
    "\n",
    "根据病人的临床病史，我们可能想预测他们在下一年心脏病发作的*概率*。\n",
    "在飞机喷气发动机的异常检测中，我们想要评估一组发动机读数为正常运行情况的概率有多大。\n",
    "在强化学习中，我们希望智能体（agent）能在一个环境中智能地行动。\n",
    "这意味着我们需要考虑在每种可行的行为下获得高奖励的概率。\n",
    "当我们建立推荐系统时，我们也需要考虑概率。\n",
    "例如，假设我们为一家大型在线书店工作，我们可能希望估计某些用户购买特定图书的概率。\n",
    "为此，我们需要使用概率学。\n",
    "有完整的课程、专业、论文、职业、甚至院系，都致力于概率学的工作。\n",
    "所以很自然地，我们在这部分的目标不是教授整个科目。\n",
    "相反，我们希望教给读者基础的概率知识，使读者能够开始构建第一个深度学习模型，\n",
    "以便读者可以开始自己探索它。\n",
    "\n",
    "现在让我们更认真地考虑第一个例子：根据照片区分猫和狗。\n",
    "这听起来可能很简单，但对于机器却可能是一个艰巨的挑战。\n",
    "首先，问题的难度可能取决于图像的分辨率。\n",
    "\n",
    "![不同分辨率的图像 ($10 \\times 10$, $20 \\times 20$, $40 \\times 40$, $80 \\times 80$, 和 $160 \\times 160$ pixels)](../img/cat-dog-pixels.png)\n",
    ":width:`300px`\n",
    ":label:`fig_cat_dog`\n",
    "\n",
    "如 :numref:`fig_cat_dog`所示，虽然人类很容易以$160 \\times 160$像素的分辨率识别猫和狗，\n",
    "但它在$40\\times40$像素上变得具有挑战性，而且在$10 \\times 10$像素下几乎是不可能的。\n",
    "换句话说，我们在很远的距离（从而降低分辨率）区分猫和狗的能力可能会变为猜测。\n",
    "概率给了我们一种正式的途径来说明我们的确定性水平。\n",
    "如果我们完全肯定图像是一只猫，我们说标签$y$是\"猫\"的*概率*，表示为$P(y=$\"猫\"$)$等于$1$。\n",
    "如果我们没有证据表明$y=$“猫”或$y=$“狗”，那么我们可以说这两种可能性是相等的，\n",
    "即$P(y=$\"猫\"$)=P(y=$\"狗\"$)=0.5$。\n",
    "如果我们不十分确定图像描绘的是一只猫，我们可以将概率赋值为$0.5<P(y=$\"猫\"$)<1$。\n",
    "\n",
    "现在考虑第二个例子：给出一些天气监测数据，我们想预测明天北京下雨的概率。\n",
    "如果是夏天，下雨的概率是0.5。\n",
    "\n",
    "在这两种情况下，我们都不确定结果，但这两种情况之间有一个关键区别。\n",
    "在第一种情况中，图像实际上是狗或猫二选一。\n",
    "在第二种情况下，结果实际上是一个随机的事件。\n",
    "因此，概率是一种灵活的语言，用于说明我们的确定程度，并且它可以有效地应用于广泛的领域中。\n",
    "\n",
    "## 基本概率论\n",
    "\n",
    "假设我们掷骰子，想知道看到1的几率有多大，而不是看到另一个数字。\n",
    "如果骰子是公平的，那么所有六个结果$\\{1, \\ldots, 6\\}$都有相同的可能发生，\n",
    "因此我们可以说$1$发生的概率为$\\frac{1}{6}$。\n",
    "\n",
    "然而现实生活中，对于我们从工厂收到的真实骰子，我们需要检查它是否有瑕疵。\n",
    "检查骰子的唯一方法是多次投掷并记录结果。\n",
    "对于每个骰子，我们将观察到$\\{1, \\ldots, 6\\}$中的一个值。\n",
    "对于每个值，一种自然的方法是将它出现的次数除以投掷的总次数，\n",
    "即此*事件*（event）概率的*估计值*。\n",
    "*大数定律*（law of large numbers）告诉我们：\n",
    "随着投掷次数的增加，这个估计值会越来越接近真实的潜在概率。\n",
    "让我们用代码试一试！\n",
    "\n",
    "首先，我们导入必要的软件包。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c265b497",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-12-07T16:49:40.290547Z",
     "iopub.status.busy": "2022-12-07T16:49:40.289989Z",
     "iopub.status.idle": "2022-12-07T16:49:42.806841Z",
     "shell.execute_reply": "2022-12-07T16:49:42.805933Z"
    },
    "origin_pos": 2,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import torch\n",
    "from torch.distributions import multinomial\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b1b8ee3",
   "metadata": {
    "origin_pos": 5
   },
   "source": [
    "在统计学中，我们把从概率分布中抽取样本的过程称为*抽样*（sampling）。\n",
    "笼统来说，可以把*分布*（distribution）看作对事件的概率分配，\n",
    "稍后我们将给出的更正式定义。\n",
    "将概率分配给一些离散选择的分布称为*多项分布*（multinomial distribution）。\n",
    "\n",
    "为了抽取一个样本，即掷骰子，我们只需传入一个概率向量。\n",
    "输出是另一个相同长度的向量：它在索引$i$处的值是采样结果中$i$出现的次数。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1b726615",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-12-07T16:49:42.813099Z",
     "iopub.status.busy": "2022-12-07T16:49:42.812207Z",
     "iopub.status.idle": "2022-12-07T16:49:42.844262Z",
     "shell.execute_reply": "2022-12-07T16:49:42.843447Z"
    },
    "origin_pos": 7,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0., 1., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fair_probs = torch.ones([6]) / 6\n",
    "multinomial.Multinomial(1, fair_probs).sample()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e698dc25",
   "metadata": {
    "origin_pos": 10
   },
   "source": [
    "在估计一个骰子的公平性时，我们希望从同一分布中生成多个样本。\n",
    "如果用Python的for循环来完成这个任务，速度会慢得惊人。\n",
    "因此我们使用深度学习框架的函数同时抽取多个样本，得到我们想要的任意形状的独立样本数组。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4e292aa1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-12-07T16:49:42.848069Z",
     "iopub.status.busy": "2022-12-07T16:49:42.847496Z",
     "iopub.status.idle": "2022-12-07T16:49:42.854831Z",
     "shell.execute_reply": "2022-12-07T16:49:42.853945Z"
    },
    "origin_pos": 12,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2., 4., 1., 0., 1., 2.])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multinomial.Multinomial(10, fair_probs).sample()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8040204f",
   "metadata": {
    "origin_pos": 15
   },
   "source": [
    "现在我们知道如何对骰子进行采样，我们可以模拟1000次投掷。\n",
    "然后，我们可以统计1000次投掷后，每个数字被投中了多少次。\n",
    "具体来说，我们计算相对频率，以作为真实概率的估计。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e0064629",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-12-07T16:49:42.858694Z",
     "iopub.status.busy": "2022-12-07T16:49:42.858141Z",
     "iopub.status.idle": "2022-12-07T16:49:42.865819Z",
     "shell.execute_reply": "2022-12-07T16:49:42.864984Z"
    },
    "origin_pos": 17,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.1620, 0.1600, 0.1740, 0.1680, 0.1570, 0.1790])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 将结果存储为32位浮点数以进行除法\n",
    "counts = multinomial.Multinomial(1000, fair_probs).sample()\n",
    "counts / 1000  # 相对频率作为估计值"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "beef9d67",
   "metadata": {
    "origin_pos": 20
   },
   "source": [
    "因为我们是从一个公平的骰子中生成的数据，我们知道每个结果都有真实的概率$\\frac{1}{6}$，\n",
    "大约是$0.167$，所以上面输出的估计值看起来不错。\n",
    "\n",
    "我们也可以看到这些概率如何随着时间的推移收敛到真实概率。\n",
    "让我们进行500组实验，每组抽取10个样本。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "dc8fa96c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-12-07T16:49:42.869470Z",
     "iopub.status.busy": "2022-12-07T16:49:42.868996Z",
     "iopub.status.idle": "2022-12-07T16:49:43.119932Z",
     "shell.execute_reply": "2022-12-07T16:49:43.119066Z"
    },
    "origin_pos": 22,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"392.14375pt\" height=\"294.23625pt\" viewBox=\"0 0 392.14375 294.23625\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n",
       " <metadata>\n",
       "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
       "   <cc:Work>\n",
       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
       "    <dc:date>2022-12-07T16:49:43.060705</dc:date>\n",
       "    <dc:format>image/svg+xml</dc:format>\n",
       "    <dc:creator>\n",
       "     <cc:Agent>\n",
       "      <dc:title>Matplotlib v3.5.1, https://matplotlib.org/</dc:title>\n",
       "     </cc:Agent>\n",
       "    </dc:creator>\n",
       "   </cc:Work>\n",
       "  </rdf:RDF>\n",
       " </metadata>\n",
       " <defs>\n",
       "  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 294.23625 \n",
       "L 392.14375 294.23625 \n",
       "L 392.14375 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill: #ffffff\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 50.14375 256.68 \n",
       "L 384.94375 256.68 \n",
       "L 384.94375 7.2 \n",
       "L 50.14375 7.2 \n",
       "z\n",
       "\" style=\"fill: #ffffff\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path id=\"m8f4e5043a8\" d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use xlink:href=\"#m8f4e5043a8\" x=\"65.361932\" y=\"256.68\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(62.180682 271.278438)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path id=\"DejaVuSans-30\" d=\"M 2034 4250 \n",
       "Q 1547 4250 1301 3770 \n",
       "Q 1056 3291 1056 2328 \n",
       "Q 1056 1369 1301 889 \n",
       "Q 1547 409 2034 409 \n",
       "Q 2525 409 2770 889 \n",
       "Q 3016 1369 3016 2328 \n",
       "Q 3016 3291 2770 3770 \n",
       "Q 2525 4250 2034 4250 \n",
       "z\n",
       "M 2034 4750 \n",
       "Q 2819 4750 3233 4129 \n",
       "Q 3647 3509 3647 2328 \n",
       "Q 3647 1150 3233 529 \n",
       "Q 2819 -91 2034 -91 \n",
       "Q 1250 -91 836 529 \n",
       "Q 422 1150 422 2328 \n",
       "Q 422 3509 836 4129 \n",
       "Q 1250 4750 2034 4750 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m8f4e5043a8\" x=\"126.356649\" y=\"256.68\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- 100 -->\n",
       "      <g transform=\"translate(116.812899 271.278438)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path id=\"DejaVuSans-31\" d=\"M 794 531 \n",
       "L 1825 531 \n",
       "L 1825 4091 \n",
       "L 703 3866 \n",
       "L 703 4441 \n",
       "L 1819 4666 \n",
       "L 2450 4666 \n",
       "L 2450 531 \n",
       "L 3481 531 \n",
       "L 3481 0 \n",
       "L 794 0 \n",
       "L 794 531 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-31\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m8f4e5043a8\" x=\"187.351365\" y=\"256.68\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- 200 -->\n",
       "      <g transform=\"translate(177.807615 271.278438)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path id=\"DejaVuSans-32\" d=\"M 1228 531 \n",
       "L 3431 531 \n",
       "L 3431 0 \n",
       "L 469 0 \n",
       "L 469 531 \n",
       "Q 828 903 1448 1529 \n",
       "Q 2069 2156 2228 2338 \n",
       "Q 2531 2678 2651 2914 \n",
       "Q 2772 3150 2772 3378 \n",
       "Q 2772 3750 2511 3984 \n",
       "Q 2250 4219 1831 4219 \n",
       "Q 1534 4219 1204 4116 \n",
       "Q 875 4013 500 3803 \n",
       "L 500 4441 \n",
       "Q 881 4594 1212 4672 \n",
       "Q 1544 4750 1819 4750 \n",
       "Q 2544 4750 2975 4387 \n",
       "Q 3406 4025 3406 3419 \n",
       "Q 3406 3131 3298 2873 \n",
       "Q 3191 2616 2906 2266 \n",
       "Q 2828 2175 2409 1742 \n",
       "Q 1991 1309 1228 531 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m8f4e5043a8\" x=\"248.346082\" y=\"256.68\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- 300 -->\n",
       "      <g transform=\"translate(238.802332 271.278438)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path id=\"DejaVuSans-33\" d=\"M 2597 2516 \n",
       "Q 3050 2419 3304 2112 \n",
       "Q 3559 1806 3559 1356 \n",
       "Q 3559 666 3084 287 \n",
       "Q 2609 -91 1734 -91 \n",
       "Q 1441 -91 1130 -33 \n",
       "Q 819 25 488 141 \n",
       "L 488 750 \n",
       "Q 750 597 1062 519 \n",
       "Q 1375 441 1716 441 \n",
       "Q 2309 441 2620 675 \n",
       "Q 2931 909 2931 1356 \n",
       "Q 2931 1769 2642 2001 \n",
       "Q 2353 2234 1838 2234 \n",
       "L 1294 2234 \n",
       "L 1294 2753 \n",
       "L 1863 2753 \n",
       "Q 2328 2753 2575 2939 \n",
       "Q 2822 3125 2822 3475 \n",
       "Q 2822 3834 2567 4026 \n",
       "Q 2313 4219 1838 4219 \n",
       "Q 1578 4219 1281 4162 \n",
       "Q 984 4106 628 3988 \n",
       "L 628 4550 \n",
       "Q 988 4650 1302 4700 \n",
       "Q 1616 4750 1894 4750 \n",
       "Q 2613 4750 3031 4423 \n",
       "Q 3450 4097 3450 3541 \n",
       "Q 3450 3153 3228 2886 \n",
       "Q 3006 2619 2597 2516 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-33\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m8f4e5043a8\" x=\"309.340799\" y=\"256.68\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- 400 -->\n",
       "      <g transform=\"translate(299.797049 271.278438)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path id=\"DejaVuSans-34\" d=\"M 2419 4116 \n",
       "L 825 1625 \n",
       "L 2419 1625 \n",
       "L 2419 4116 \n",
       "z\n",
       "M 2253 4666 \n",
       "L 3047 4666 \n",
       "L 3047 1625 \n",
       "L 3713 1625 \n",
       "L 3713 1100 \n",
       "L 3047 1100 \n",
       "L 3047 0 \n",
       "L 2419 0 \n",
       "L 2419 1100 \n",
       "L 313 1100 \n",
       "L 313 1709 \n",
       "L 2253 4666 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-34\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m8f4e5043a8\" x=\"370.335515\" y=\"256.68\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 500 -->\n",
       "      <g transform=\"translate(360.791765 271.278438)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path id=\"DejaVuSans-35\" d=\"M 691 4666 \n",
       "L 3169 4666 \n",
       "L 3169 4134 \n",
       "L 1269 4134 \n",
       "L 1269 2991 \n",
       "Q 1406 3038 1543 3061 \n",
       "Q 1681 3084 1819 3084 \n",
       "Q 2600 3084 3056 2656 \n",
       "Q 3513 2228 3513 1497 \n",
       "Q 3513 744 3044 326 \n",
       "Q 2575 -91 1722 -91 \n",
       "Q 1428 -91 1123 -41 \n",
       "Q 819 9 494 109 \n",
       "L 494 744 \n",
       "Q 775 591 1075 516 \n",
       "Q 1375 441 1709 441 \n",
       "Q 2250 441 2565 725 \n",
       "Q 2881 1009 2881 1497 \n",
       "Q 2881 1984 2565 2268 \n",
       "Q 2250 2553 1709 2553 \n",
       "Q 1456 2553 1204 2497 \n",
       "Q 953 2441 691 2322 \n",
       "L 691 4666 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-35\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_7\">\n",
       "     <!-- Groups of experiments -->\n",
       "     <g transform=\"translate(160.397656 284.956563)scale(0.1 -0.1)\">\n",
       "      <defs>\n",
       "       <path id=\"DejaVuSans-47\" d=\"M 3809 666 \n",
       "L 3809 1919 \n",
       "L 2778 1919 \n",
       "L 2778 2438 \n",
       "L 4434 2438 \n",
       "L 4434 434 \n",
       "Q 4069 175 3628 42 \n",
       "Q 3188 -91 2688 -91 \n",
       "Q 1594 -91 976 548 \n",
       "Q 359 1188 359 2328 \n",
       "Q 359 3472 976 4111 \n",
       "Q 1594 4750 2688 4750 \n",
       "Q 3144 4750 3555 4637 \n",
       "Q 3966 4525 4313 4306 \n",
       "L 4313 3634 \n",
       "Q 3963 3931 3569 4081 \n",
       "Q 3175 4231 2741 4231 \n",
       "Q 1884 4231 1454 3753 \n",
       "Q 1025 3275 1025 2328 \n",
       "Q 1025 1384 1454 906 \n",
       "Q 1884 428 2741 428 \n",
       "Q 3075 428 3337 486 \n",
       "Q 3600 544 3809 666 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-72\" d=\"M 2631 2963 \n",
       "Q 2534 3019 2420 3045 \n",
       "Q 2306 3072 2169 3072 \n",
       "Q 1681 3072 1420 2755 \n",
       "Q 1159 2438 1159 1844 \n",
       "L 1159 0 \n",
       "L 581 0 \n",
       "L 581 3500 \n",
       "L 1159 3500 \n",
       "L 1159 2956 \n",
       "Q 1341 3275 1631 3429 \n",
       "Q 1922 3584 2338 3584 \n",
       "Q 2397 3584 2469 3576 \n",
       "Q 2541 3569 2628 3553 \n",
       "L 2631 2963 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-6f\" d=\"M 1959 3097 \n",
       "Q 1497 3097 1228 2736 \n",
       "Q 959 2375 959 1747 \n",
       "Q 959 1119 1226 758 \n",
       "Q 1494 397 1959 397 \n",
       "Q 2419 397 2687 759 \n",
       "Q 2956 1122 2956 1747 \n",
       "Q 2956 2369 2687 2733 \n",
       "Q 2419 3097 1959 3097 \n",
       "z\n",
       "M 1959 3584 \n",
       "Q 2709 3584 3137 3096 \n",
       "Q 3566 2609 3566 1747 \n",
       "Q 3566 888 3137 398 \n",
       "Q 2709 -91 1959 -91 \n",
       "Q 1206 -91 779 398 \n",
       "Q 353 888 353 1747 \n",
       "Q 353 2609 779 3096 \n",
       "Q 1206 3584 1959 3584 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-75\" d=\"M 544 1381 \n",
       "L 544 3500 \n",
       "L 1119 3500 \n",
       "L 1119 1403 \n",
       "Q 1119 906 1312 657 \n",
       "Q 1506 409 1894 409 \n",
       "Q 2359 409 2629 706 \n",
       "Q 2900 1003 2900 1516 \n",
       "L 2900 3500 \n",
       "L 3475 3500 \n",
       "L 3475 0 \n",
       "L 2900 0 \n",
       "L 2900 538 \n",
       "Q 2691 219 2414 64 \n",
       "Q 2138 -91 1772 -91 \n",
       "Q 1169 -91 856 284 \n",
       "Q 544 659 544 1381 \n",
       "z\n",
       "M 1991 3584 \n",
       "L 1991 3584 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-70\" d=\"M 1159 525 \n",
       "L 1159 -1331 \n",
       "L 581 -1331 \n",
       "L 581 3500 \n",
       "L 1159 3500 \n",
       "L 1159 2969 \n",
       "Q 1341 3281 1617 3432 \n",
       "Q 1894 3584 2278 3584 \n",
       "Q 2916 3584 3314 3078 \n",
       "Q 3713 2572 3713 1747 \n",
       "Q 3713 922 3314 415 \n",
       "Q 2916 -91 2278 -91 \n",
       "Q 1894 -91 1617 61 \n",
       "Q 1341 213 1159 525 \n",
       "z\n",
       "M 3116 1747 \n",
       "Q 3116 2381 2855 2742 \n",
       "Q 2594 3103 2138 3103 \n",
       "Q 1681 3103 1420 2742 \n",
       "Q 1159 2381 1159 1747 \n",
       "Q 1159 1113 1420 752 \n",
       "Q 1681 391 2138 391 \n",
       "Q 2594 391 2855 752 \n",
       "Q 3116 1113 3116 1747 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-73\" d=\"M 2834 3397 \n",
       "L 2834 2853 \n",
       "Q 2591 2978 2328 3040 \n",
       "Q 2066 3103 1784 3103 \n",
       "Q 1356 3103 1142 2972 \n",
       "Q 928 2841 928 2578 \n",
       "Q 928 2378 1081 2264 \n",
       "Q 1234 2150 1697 2047 \n",
       "L 1894 2003 \n",
       "Q 2506 1872 2764 1633 \n",
       "Q 3022 1394 3022 966 \n",
       "Q 3022 478 2636 193 \n",
       "Q 2250 -91 1575 -91 \n",
       "Q 1294 -91 989 -36 \n",
       "Q 684 19 347 128 \n",
       "L 347 722 \n",
       "Q 666 556 975 473 \n",
       "Q 1284 391 1588 391 \n",
       "Q 1994 391 2212 530 \n",
       "Q 2431 669 2431 922 \n",
       "Q 2431 1156 2273 1281 \n",
       "Q 2116 1406 1581 1522 \n",
       "L 1381 1569 \n",
       "Q 847 1681 609 1914 \n",
       "Q 372 2147 372 2553 \n",
       "Q 372 3047 722 3315 \n",
       "Q 1072 3584 1716 3584 \n",
       "Q 2034 3584 2315 3537 \n",
       "Q 2597 3491 2834 3397 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-20\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-66\" d=\"M 2375 4863 \n",
       "L 2375 4384 \n",
       "L 1825 4384 \n",
       "Q 1516 4384 1395 4259 \n",
       "Q 1275 4134 1275 3809 \n",
       "L 1275 3500 \n",
       "L 2222 3500 \n",
       "L 2222 3053 \n",
       "L 1275 3053 \n",
       "L 1275 0 \n",
       "L 697 0 \n",
       "L 697 3053 \n",
       "L 147 3053 \n",
       "L 147 3500 \n",
       "L 697 3500 \n",
       "L 697 3744 \n",
       "Q 697 4328 969 4595 \n",
       "Q 1241 4863 1831 4863 \n",
       "L 2375 4863 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-65\" d=\"M 3597 1894 \n",
       "L 3597 1613 \n",
       "L 953 1613 \n",
       "Q 991 1019 1311 708 \n",
       "Q 1631 397 2203 397 \n",
       "Q 2534 397 2845 478 \n",
       "Q 3156 559 3463 722 \n",
       "L 3463 178 \n",
       "Q 3153 47 2828 -22 \n",
       "Q 2503 -91 2169 -91 \n",
       "Q 1331 -91 842 396 \n",
       "Q 353 884 353 1716 \n",
       "Q 353 2575 817 3079 \n",
       "Q 1281 3584 2069 3584 \n",
       "Q 2775 3584 3186 3129 \n",
       "Q 3597 2675 3597 1894 \n",
       "z\n",
       "M 3022 2063 \n",
       "Q 3016 2534 2758 2815 \n",
       "Q 2500 3097 2075 3097 \n",
       "Q 1594 3097 1305 2825 \n",
       "Q 1016 2553 972 2059 \n",
       "L 3022 2063 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-78\" d=\"M 3513 3500 \n",
       "L 2247 1797 \n",
       "L 3578 0 \n",
       "L 2900 0 \n",
       "L 1881 1375 \n",
       "L 863 0 \n",
       "L 184 0 \n",
       "L 1544 1831 \n",
       "L 300 3500 \n",
       "L 978 3500 \n",
       "L 1906 2253 \n",
       "L 2834 3500 \n",
       "L 3513 3500 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-69\" d=\"M 603 3500 \n",
       "L 1178 3500 \n",
       "L 1178 0 \n",
       "L 603 0 \n",
       "L 603 3500 \n",
       "z\n",
       "M 603 4863 \n",
       "L 1178 4863 \n",
       "L 1178 4134 \n",
       "L 603 4134 \n",
       "L 603 4863 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-6d\" d=\"M 3328 2828 \n",
       "Q 3544 3216 3844 3400 \n",
       "Q 4144 3584 4550 3584 \n",
       "Q 5097 3584 5394 3201 \n",
       "Q 5691 2819 5691 2113 \n",
       "L 5691 0 \n",
       "L 5113 0 \n",
       "L 5113 2094 \n",
       "Q 5113 2597 4934 2840 \n",
       "Q 4756 3084 4391 3084 \n",
       "Q 3944 3084 3684 2787 \n",
       "Q 3425 2491 3425 1978 \n",
       "L 3425 0 \n",
       "L 2847 0 \n",
       "L 2847 2094 \n",
       "Q 2847 2600 2669 2842 \n",
       "Q 2491 3084 2119 3084 \n",
       "Q 1678 3084 1418 2786 \n",
       "Q 1159 2488 1159 1978 \n",
       "L 1159 0 \n",
       "L 581 0 \n",
       "L 581 3500 \n",
       "L 1159 3500 \n",
       "L 1159 2956 \n",
       "Q 1356 3278 1631 3431 \n",
       "Q 1906 3584 2284 3584 \n",
       "Q 2666 3584 2933 3390 \n",
       "Q 3200 3197 3328 2828 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-6e\" d=\"M 3513 2113 \n",
       "L 3513 0 \n",
       "L 2938 0 \n",
       "L 2938 2094 \n",
       "Q 2938 2591 2744 2837 \n",
       "Q 2550 3084 2163 3084 \n",
       "Q 1697 3084 1428 2787 \n",
       "Q 1159 2491 1159 1978 \n",
       "L 1159 0 \n",
       "L 581 0 \n",
       "L 581 3500 \n",
       "L 1159 3500 \n",
       "L 1159 2956 \n",
       "Q 1366 3272 1645 3428 \n",
       "Q 1925 3584 2291 3584 \n",
       "Q 2894 3584 3203 3211 \n",
       "Q 3513 2838 3513 2113 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-74\" d=\"M 1172 4494 \n",
       "L 1172 3500 \n",
       "L 2356 3500 \n",
       "L 2356 3053 \n",
       "L 1172 3053 \n",
       "L 1172 1153 \n",
       "Q 1172 725 1289 603 \n",
       "Q 1406 481 1766 481 \n",
       "L 2356 481 \n",
       "L 2356 0 \n",
       "L 1766 0 \n",
       "Q 1100 0 847 248 \n",
       "Q 594 497 594 1153 \n",
       "L 594 3053 \n",
       "L 172 3053 \n",
       "L 172 3500 \n",
       "L 594 3500 \n",
       "L 594 4494 \n",
       "L 1172 4494 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-47\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-72\" x=\"77.490234\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-6f\" x=\"116.353516\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-75\" x=\"177.535156\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-70\" x=\"240.914062\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-73\" x=\"304.390625\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-20\" x=\"356.490234\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-6f\" x=\"388.277344\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-66\" x=\"449.458984\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-20\" x=\"484.664062\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-65\" x=\"516.451172\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-78\" x=\"576.224609\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-70\" x=\"635.404297\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-65\" x=\"698.880859\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-72\" x=\"760.404297\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-69\" x=\"801.517578\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-6d\" x=\"829.300781\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-65\" x=\"926.712891\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-6e\" x=\"988.236328\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-74\" x=\"1051.615234\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-73\" x=\"1090.824219\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <defs>\n",
       "       <path id=\"m233694d1f3\" d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use xlink:href=\"#m233694d1f3\" x=\"50.14375\" y=\"212.940005\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- 0.10 -->\n",
       "      <g transform=\"translate(20.878125 216.739223)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path id=\"DejaVuSans-2e\" d=\"M 684 794 \n",
       "L 1344 794 \n",
       "L 1344 0 \n",
       "L 684 0 \n",
       "L 684 794 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-30\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-2e\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"95.410156\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"159.033203\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m233694d1f3\" x=\"50.14375\" y=\"164.340006\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- 0.15 -->\n",
       "      <g transform=\"translate(20.878125 168.139225)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-30\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-2e\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"95.410156\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-35\" x=\"159.033203\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m233694d1f3\" x=\"50.14375\" y=\"115.740008\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- 0.20 -->\n",
       "      <g transform=\"translate(20.878125 119.539227)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-30\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-2e\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-32\" x=\"95.410156\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"159.033203\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m233694d1f3\" x=\"50.14375\" y=\"67.14001\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- 0.25 -->\n",
       "      <g transform=\"translate(20.878125 70.939229)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-30\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-2e\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-32\" x=\"95.410156\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-35\" x=\"159.033203\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m233694d1f3\" x=\"50.14375\" y=\"18.540012\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- 0.30 -->\n",
       "      <g transform=\"translate(20.878125 22.33923)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-30\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-2e\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-33\" x=\"95.410156\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"159.033203\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_13\">\n",
       "     <!-- Estimated probability -->\n",
       "     <g transform=\"translate(14.798438 185.463438)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <defs>\n",
       "       <path id=\"DejaVuSans-45\" d=\"M 628 4666 \n",
       "L 3578 4666 \n",
       "L 3578 4134 \n",
       "L 1259 4134 \n",
       "L 1259 2753 \n",
       "L 3481 2753 \n",
       "L 3481 2222 \n",
       "L 1259 2222 \n",
       "L 1259 531 \n",
       "L 3634 531 \n",
       "L 3634 0 \n",
       "L 628 0 \n",
       "L 628 4666 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-61\" d=\"M 2194 1759 \n",
       "Q 1497 1759 1228 1600 \n",
       "Q 959 1441 959 1056 \n",
       "Q 959 750 1161 570 \n",
       "Q 1363 391 1709 391 \n",
       "Q 2188 391 2477 730 \n",
       "Q 2766 1069 2766 1631 \n",
       "L 2766 1759 \n",
       "L 2194 1759 \n",
       "z\n",
       "M 3341 1997 \n",
       "L 3341 0 \n",
       "L 2766 0 \n",
       "L 2766 531 \n",
       "Q 2569 213 2275 61 \n",
       "Q 1981 -91 1556 -91 \n",
       "Q 1019 -91 701 211 \n",
       "Q 384 513 384 1019 \n",
       "Q 384 1609 779 1909 \n",
       "Q 1175 2209 1959 2209 \n",
       "L 2766 2209 \n",
       "L 2766 2266 \n",
       "Q 2766 2663 2505 2880 \n",
       "Q 2244 3097 1772 3097 \n",
       "Q 1472 3097 1187 3025 \n",
       "Q 903 2953 641 2809 \n",
       "L 641 3341 \n",
       "Q 956 3463 1253 3523 \n",
       "Q 1550 3584 1831 3584 \n",
       "Q 2591 3584 2966 3190 \n",
       "Q 3341 2797 3341 1997 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-64\" d=\"M 2906 2969 \n",
       "L 2906 4863 \n",
       "L 3481 4863 \n",
       "L 3481 0 \n",
       "L 2906 0 \n",
       "L 2906 525 \n",
       "Q 2725 213 2448 61 \n",
       "Q 2172 -91 1784 -91 \n",
       "Q 1150 -91 751 415 \n",
       "Q 353 922 353 1747 \n",
       "Q 353 2572 751 3078 \n",
       "Q 1150 3584 1784 3584 \n",
       "Q 2172 3584 2448 3432 \n",
       "Q 2725 3281 2906 2969 \n",
       "z\n",
       "M 947 1747 \n",
       "Q 947 1113 1208 752 \n",
       "Q 1469 391 1925 391 \n",
       "Q 2381 391 2643 752 \n",
       "Q 2906 1113 2906 1747 \n",
       "Q 2906 2381 2643 2742 \n",
       "Q 2381 3103 1925 3103 \n",
       "Q 1469 3103 1208 2742 \n",
       "Q 947 2381 947 1747 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-62\" d=\"M 3116 1747 \n",
       "Q 3116 2381 2855 2742 \n",
       "Q 2594 3103 2138 3103 \n",
       "Q 1681 3103 1420 2742 \n",
       "Q 1159 2381 1159 1747 \n",
       "Q 1159 1113 1420 752 \n",
       "Q 1681 391 2138 391 \n",
       "Q 2594 391 2855 752 \n",
       "Q 3116 1113 3116 1747 \n",
       "z\n",
       "M 1159 2969 \n",
       "Q 1341 3281 1617 3432 \n",
       "Q 1894 3584 2278 3584 \n",
       "Q 2916 3584 3314 3078 \n",
       "Q 3713 2572 3713 1747 \n",
       "Q 3713 922 3314 415 \n",
       "Q 2916 -91 2278 -91 \n",
       "Q 1894 -91 1617 61 \n",
       "Q 1341 213 1159 525 \n",
       "L 1159 0 \n",
       "L 581 0 \n",
       "L 581 4863 \n",
       "L 1159 4863 \n",
       "L 1159 2969 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-6c\" d=\"M 603 4863 \n",
       "L 1178 4863 \n",
       "L 1178 0 \n",
       "L 603 0 \n",
       "L 603 4863 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-79\" d=\"M 2059 -325 \n",
       "Q 1816 -950 1584 -1140 \n",
       "Q 1353 -1331 966 -1331 \n",
       "L 506 -1331 \n",
       "L 506 -850 \n",
       "L 844 -850 \n",
       "Q 1081 -850 1212 -737 \n",
       "Q 1344 -625 1503 -206 \n",
       "L 1606 56 \n",
       "L 191 3500 \n",
       "L 800 3500 \n",
       "L 1894 763 \n",
       "L 2988 3500 \n",
       "L 3597 3500 \n",
       "L 2059 -325 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-45\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-73\" x=\"63.183594\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-74\" x=\"115.283203\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-69\" x=\"154.492188\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-6d\" x=\"182.275391\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-61\" x=\"279.6875\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-74\" x=\"340.966797\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-65\" x=\"380.175781\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-64\" x=\"441.699219\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-20\" x=\"505.175781\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-70\" x=\"536.962891\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-72\" x=\"600.439453\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-6f\" x=\"639.302734\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-62\" x=\"700.484375\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-61\" x=\"763.960938\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-62\" x=\"825.240234\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-69\" x=\"888.716797\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-6c\" x=\"916.5\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-69\" x=\"944.283203\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-74\" x=\"972.066406\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-79\" x=\"1011.275391\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_12\">\n",
       "    <path d=\"M 65.361932 212.940003 \n",
       "L 65.971879 164.340001 \n",
       "L 66.581826 83.340008 \n",
       "L 67.191773 115.740005 \n",
       "L 67.80172 135.18 \n",
       "L 68.411668 115.740005 \n",
       "L 69.021615 129.625718 \n",
       "L 69.631562 127.890008 \n",
       "L 70.241509 148.140002 \n",
       "L 70.851456 164.340001 \n",
       "L 71.461403 151.085468 \n",
       "L 72.071351 156.240009 \n",
       "L 72.681298 145.647695 \n",
       "L 73.291245 150.454288 \n",
       "L 74.511139 133.965002 \n",
       "L 75.121086 132.892945 \n",
       "L 75.731034 142.740003 \n",
       "L 76.950928 140.04001 \n",
       "L 77.560875 148.140002 \n",
       "L 78.170822 151.085468 \n",
       "L 78.780769 149.548709 \n",
       "L 79.390717 152.190013 \n",
       "L 80.000664 150.732002 \n",
       "L 80.610611 156.863078 \n",
       "L 81.220558 151.740011 \n",
       "L 81.830505 157.397144 \n",
       "L 83.0504 161.100004 \n",
       "L 83.660347 159.636779 \n",
       "L 84.270294 164.340001 \n",
       "L 85.490188 161.481177 \n",
       "L 86.100135 162.951441 \n",
       "L 86.710083 158.940001 \n",
       "L 87.32003 157.772437 \n",
       "L 87.929977 154.108423 \n",
       "L 88.539924 155.616924 \n",
       "L 89.149871 152.190013 \n",
       "L 89.759819 153.671718 \n",
       "L 90.979713 151.907446 \n",
       "L 92.809554 143.209572 \n",
       "L 93.419502 142.625116 \n",
       "L 94.639396 145.495106 \n",
       "L 96.469237 154.993855 \n",
       "L 97.079185 154.253219 \n",
       "L 97.689132 155.340006 \n",
       "L 98.299079 154.62001 \n",
       "L 99.518973 149.845267 \n",
       "L 100.12892 150.933112 \n",
       "L 101.348815 149.76 \n",
       "L 101.958762 147.608862 \n",
       "L 103.178656 152.768573 \n",
       "L 103.788603 152.190013 \n",
       "L 105.008498 154.03092 \n",
       "L 105.618445 153.459413 \n",
       "L 106.228392 155.763531 \n",
       "L 106.838339 155.183478 \n",
       "L 107.448286 156.008584 \n",
       "L 108.058234 155.441408 \n",
       "L 108.668181 156.240009 \n",
       "L 109.278128 154.353709 \n",
       "L 109.888075 153.831896 \n",
       "L 110.498022 155.916003 \n",
       "L 111.107969 156.666328 \n",
       "L 111.717917 156.134812 \n",
       "L 112.937811 157.572921 \n",
       "L 113.547758 155.835009 \n",
       "L 114.157705 152.940005 \n",
       "L 114.767652 151.300989 \n",
       "L 115.987547 152.768573 \n",
       "L 118.427335 146.667276 \n",
       "L 119.64723 148.140002 \n",
       "L 120.257177 145.647695 \n",
       "L 122.087018 150.897452 \n",
       "L 122.696966 149.504214 \n",
       "L 123.306913 149.152501 \n",
       "L 125.136754 151.085468 \n",
       "L 126.966596 150.045884 \n",
       "L 127.576543 150.656512 \n",
       "L 128.796437 149.991439 \n",
       "L 130.016332 151.168041 \n",
       "L 130.626279 152.640014 \n",
       "L 131.846173 153.736375 \n",
       "L 132.45612 151.642708 \n",
       "L 133.066067 152.190013 \n",
       "L 133.676015 151.007269 \n",
       "L 134.895909 150.393919 \n",
       "L 135.505856 150.933112 \n",
       "L 136.72575 150.33662 \n",
       "L 137.335698 150.862691 \n",
       "L 137.945645 150.57 \n",
       "L 138.555592 151.085468 \n",
       "L 139.165539 150.795746 \n",
       "L 140.385433 151.798077 \n",
       "L 140.995381 153.064813 \n",
       "L 142.825222 152.190013 \n",
       "L 143.435169 153.414426 \n",
       "L 144.655064 154.32322 \n",
       "L 145.265011 154.03092 \n",
       "L 145.874958 152.281363 \n",
       "L 146.484905 152.734043 \n",
       "L 147.094852 151.740011 \n",
       "L 147.704799 152.190013 \n",
       "L 148.314747 151.923943 \n",
       "L 148.924694 153.070447 \n",
       "L 149.534641 152.102602 \n",
       "L 150.144588 151.842862 \n",
       "L 151.364482 152.703381 \n",
       "L 151.97443 150.405737 \n",
       "L 152.584377 151.515004 \n",
       "L 153.194324 149.927594 \n",
       "L 153.804271 149.693432 \n",
       "L 155.024165 151.861633 \n",
       "L 156.24406 150.084006 \n",
       "L 157.463954 149.632107 \n",
       "L 158.073901 148.775296 \n",
       "L 158.683848 148.560789 \n",
       "L 159.903743 149.386156 \n",
       "L 161.733584 152.41925 \n",
       "L 162.343531 152.190013 \n",
       "L 162.953479 150.756162 \n",
       "L 163.563426 151.740011 \n",
       "L 164.173373 151.519146 \n",
       "L 164.78332 149.522928 \n",
       "L 165.393267 149.318183 \n",
       "L 166.003214 148.530373 \n",
       "L 166.613162 148.916051 \n",
       "L 167.223109 148.718577 \n",
       "L 167.833056 147.948293 \n",
       "L 168.443003 147.758829 \n",
       "L 169.05295 146.434737 \n",
       "L 169.662897 145.691175 \n",
       "L 170.882792 146.464139 \n",
       "L 172.712633 145.943398 \n",
       "L 173.32258 146.319778 \n",
       "L 173.932528 147.234974 \n",
       "L 174.542475 147.060008 \n",
       "L 175.152422 147.960995 \n",
       "L 175.762369 147.783958 \n",
       "L 176.372316 146.015413 \n",
       "L 178.812105 145.367822 \n",
       "L 179.422052 146.244259 \n",
       "L 180.031999 145.568583 \n",
       "L 181.861841 146.621261 \n",
       "L 183.081735 148.307016 \n",
       "L 183.691682 148.638466 \n",
       "L 185.521524 151.085468 \n",
       "L 186.741418 151.704004 \n",
       "L 187.351365 150.074331 \n",
       "L 187.961312 150.385547 \n",
       "L 189.181207 150.045884 \n",
       "L 189.791154 150.826843 \n",
       "L 191.011048 151.42697 \n",
       "L 191.620995 150.788084 \n",
       "L 192.230943 150.620389 \n",
       "L 192.84089 150.91715 \n",
       "L 193.450837 151.671763 \n",
       "L 194.060784 151.502272 \n",
       "L 195.280678 150.259638 \n",
       "L 196.500573 151.740011 \n",
       "L 197.11052 152.022028 \n",
       "L 197.720467 151.409734 \n",
       "L 200.770203 150.609961 \n",
       "L 201.38015 150.888226 \n",
       "L 201.990097 151.596012 \n",
       "L 204.429886 150.969698 \n",
       "L 205.039833 150.393919 \n",
       "L 205.64978 151.085468 \n",
       "L 206.259727 151.352074 \n",
       "L 206.869675 150.364893 \n",
       "L 207.479622 151.047694 \n",
       "L 208.089569 150.483835 \n",
       "L 209.309463 150.190637 \n",
       "L 209.91941 150.862691 \n",
       "L 210.529358 150.309043 \n",
       "L 211.139305 150.165 \n",
       "L 211.749252 150.828798 \n",
       "L 212.969146 151.340009 \n",
       "L 213.579093 151.194112 \n",
       "L 214.189041 151.446132 \n",
       "L 215.408935 150.369962 \n",
       "L 216.018882 150.230323 \n",
       "L 217.238776 151.509601 \n",
       "L 217.848724 150.592595 \n",
       "L 219.068618 150.317081 \n",
       "L 220.288512 150.808246 \n",
       "L 220.898459 150.671257 \n",
       "L 221.508407 150.913544 \n",
       "L 222.118354 150.777221 \n",
       "L 222.728301 149.891355 \n",
       "L 223.338248 149.76 \n",
       "L 223.948195 149.257249 \n",
       "L 224.558142 148.38733 \n",
       "L 225.16809 149.002361 \n",
       "L 225.778037 148.876365 \n",
       "L 226.997931 150.088873 \n",
       "L 229.43772 149.580009 \n",
       "L 230.047667 149.096463 \n",
       "L 231.877508 148.731251 \n",
       "L 232.487456 148.964731 \n",
       "L 233.70735 148.724849 \n",
       "L 234.927244 149.185162 \n",
       "L 235.537191 148.718577 \n",
       "L 236.147139 148.601214 \n",
       "L 236.757086 148.829365 \n",
       "L 237.367033 149.399365 \n",
       "L 237.97698 149.280858 \n",
       "L 238.586927 148.822108 \n",
       "L 239.196874 149.386156 \n",
       "L 239.806822 149.607601 \n",
       "L 240.416769 148.815011 \n",
       "L 242.856557 149.693432 \n",
       "L 243.466505 150.241026 \n",
       "L 244.076452 150.123677 \n",
       "L 244.686399 150.33662 \n",
       "L 245.296346 149.891355 \n",
       "L 245.906293 150.103646 \n",
       "L 246.51624 149.662162 \n",
       "L 247.126188 149.873786 \n",
       "L 247.736135 149.76 \n",
       "L 248.956029 150.178412 \n",
       "L 249.565976 149.423177 \n",
       "L 250.175923 149.951855 \n",
       "L 250.785871 150.158366 \n",
       "L 251.395818 149.728237 \n",
       "L 252.005765 150.250759 \n",
       "L 252.615712 150.454288 \n",
       "L 253.225659 150.971074 \n",
       "L 253.835606 150.857433 \n",
       "L 254.445554 150.431968 \n",
       "L 255.055501 150.943859 \n",
       "L 255.665448 150.831377 \n",
       "L 256.275395 151.029184 \n",
       "L 256.885342 151.534296 \n",
       "L 257.495289 151.728613 \n",
       "L 258.105237 152.228337 \n",
       "L 258.715184 151.807927 \n",
       "L 259.325131 152.304276 \n",
       "L 261.154972 151.963614 \n",
       "L 261.76492 152.453316 \n",
       "L 262.984814 152.825538 \n",
       "L 263.594761 152.115464 \n",
       "L 264.204708 152.59872 \n",
       "L 264.814655 152.486354 \n",
       "L 265.424603 152.96554 \n",
       "L 266.03455 153.147284 \n",
       "L 267.254444 152.336387 \n",
       "L 267.864391 152.226498 \n",
       "L 268.474338 152.699282 \n",
       "L 269.084286 152.879114 \n",
       "L 269.694233 152.768573 \n",
       "L 270.30418 152.947131 \n",
       "L 270.914127 152.549475 \n",
       "L 271.524074 153.014336 \n",
       "L 272.134021 152.904707 \n",
       "L 272.743969 152.510687 \n",
       "L 273.353916 152.97158 \n",
       "L 273.963863 152.863037 \n",
       "L 274.57381 153.037684 \n",
       "L 275.183757 152.366094 \n",
       "L 277.013599 152.888283 \n",
       "L 278.233493 152.676006 \n",
       "L 278.84344 152.293848 \n",
       "L 279.453387 151.63774 \n",
       "L 280.063335 151.811388 \n",
       "L 280.673282 152.258652 \n",
       "L 281.283229 152.429591 \n",
       "L 281.893176 152.872597 \n",
       "L 282.503123 153.040842 \n",
       "L 283.723018 152.833041 \n",
       "L 284.942912 153.166041 \n",
       "L 285.552859 153.599675 \n",
       "L 286.772753 152.857591 \n",
       "L 287.992648 153.185913 \n",
       "L 288.602595 153.61358 \n",
       "L 289.212542 153.774786 \n",
       "L 290.432436 154.62001 \n",
       "L 291.652331 154.410978 \n",
       "L 292.262278 153.786112 \n",
       "L 292.872225 153.684392 \n",
       "L 294.092119 153.999577 \n",
       "L 294.702067 153.898102 \n",
       "L 295.312014 154.054297 \n",
       "L 296.531908 153.852637 \n",
       "L 297.141855 154.262836 \n",
       "L 297.751802 153.907546 \n",
       "L 299.581644 153.610133 \n",
       "L 300.191591 153.763836 \n",
       "L 300.801538 153.414426 \n",
       "L 302.021433 153.220732 \n",
       "L 302.63138 153.623081 \n",
       "L 303.241327 153.774786 \n",
       "L 303.851274 152.933878 \n",
       "L 305.071168 153.23849 \n",
       "L 305.681116 153.143547 \n",
       "L 306.291063 152.558194 \n",
       "L 306.90101 152.220617 \n",
       "L 308.730851 151.947001 \n",
       "L 309.340799 152.3415 \n",
       "L 309.950746 152.250454 \n",
       "L 310.560693 152.401043 \n",
       "L 311.780587 152.220009 \n",
       "L 313.000482 151.563105 \n",
       "L 314.830323 152.012208 \n",
       "L 315.44027 151.923943 \n",
       "L 316.050217 151.364284 \n",
       "L 316.660165 151.042668 \n",
       "L 317.880059 150.87254 \n",
       "L 319.099953 151.170228 \n",
       "L 319.7099 151.085468 \n",
       "L 320.319848 151.233088 \n",
       "L 321.539742 151.987991 \n",
       "L 322.149689 151.671763 \n",
       "L 323.369583 152.41925 \n",
       "L 324.589478 152.24705 \n",
       "L 325.199425 152.389181 \n",
       "L 326.419319 151.765184 \n",
       "L 327.639214 151.598011 \n",
       "L 328.249161 151.740011 \n",
       "L 329.469055 150.678253 \n",
       "L 330.079002 150.821383 \n",
       "L 331.298897 149.771124 \n",
       "L 331.908844 149.693432 \n",
       "L 332.518791 149.837504 \n",
       "L 333.128738 149.76 \n",
       "L 333.738685 150.123677 \n",
       "L 334.348632 149.825975 \n",
       "L 334.95858 150.187856 \n",
       "L 335.568527 150.11028 \n",
       "L 336.178474 150.251469 \n",
       "L 337.398368 150.097056 \n",
       "L 338.008315 150.237333 \n",
       "L 338.618263 150.160496 \n",
       "L 339.22821 149.868007 \n",
       "L 339.838157 150.22337 \n",
       "L 340.448104 150.362126 \n",
       "L 341.667998 151.066002 \n",
       "L 342.277946 150.988353 \n",
       "L 344.107787 152.030834 \n",
       "L 344.717734 152.163536 \n",
       "L 345.327681 152.084352 \n",
       "L 346.547576 152.3478 \n",
       "L 347.157523 152.058803 \n",
       "L 347.76747 151.980517 \n",
       "L 348.377417 152.320658 \n",
       "L 348.987365 152.450738 \n",
       "L 349.597312 152.372133 \n",
       "L 350.817206 153.044912 \n",
       "L 351.427153 153.172342 \n",
       "L 352.0371 153.505617 \n",
       "L 352.647048 152.80781 \n",
       "L 353.256995 152.729437 \n",
       "L 353.866942 152.856462 \n",
       "L 354.476889 152.778321 \n",
       "L 355.086836 152.29211 \n",
       "L 356.306731 152.139174 \n",
       "L 356.916678 152.469031 \n",
       "L 358.136572 151.912153 \n",
       "L 359.356466 151.76236 \n",
       "L 359.966414 151.286288 \n",
       "L 360.576361 151.413413 \n",
       "L 361.186308 151.740011 \n",
       "L 361.796255 151.865674 \n",
       "L 362.406202 151.393281 \n",
       "L 363.016149 151.121606 \n",
       "L 363.626097 151.446132 \n",
       "L 364.236044 150.977476 \n",
       "L 365.455938 150.834534 \n",
       "L 366.065885 151.157004 \n",
       "L 366.675832 151.085468 \n",
       "L 367.28578 151.406142 \n",
       "L 367.895727 151.334374 \n",
       "L 369.115621 151.581296 \n",
       "L 369.725568 151.315212 \n",
       "L 369.725568 151.315212 \n",
       "\" clip-path=\"url(#p5d83ec11e7)\" style=\"fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_13\">\n",
       "    <path d=\"M 65.361932 212.940003 \n",
       "L 65.971879 164.340001 \n",
       "L 66.581826 148.140002 \n",
       "L 67.191773 115.740005 \n",
       "L 68.411668 115.740005 \n",
       "L 69.021615 129.625718 \n",
       "L 69.631562 140.04001 \n",
       "L 70.241509 158.940001 \n",
       "L 70.851456 135.18 \n",
       "L 71.461403 133.412729 \n",
       "L 72.071351 115.740005 \n",
       "L 73.291245 129.625718 \n",
       "L 74.511139 127.890008 \n",
       "L 75.121086 115.740005 \n",
       "L 75.731034 115.740005 \n",
       "L 76.340981 120.855801 \n",
       "L 76.950928 120.600015 \n",
       "L 77.560875 111.111434 \n",
       "L 78.170822 120.158183 \n",
       "L 78.780769 124.192188 \n",
       "L 79.390717 123.840012 \n",
       "L 80.000664 127.404014 \n",
       "L 80.610611 123.216928 \n",
       "L 81.830505 129.625718 \n",
       "L 83.0504 135.18 \n",
       "L 83.660347 134.552904 \n",
       "L 84.270294 127.890008 \n",
       "L 84.880241 130.467278 \n",
       "L 85.490188 130.034121 \n",
       "L 86.100135 132.402867 \n",
       "L 86.710083 131.940004 \n",
       "L 87.32003 136.756228 \n",
       "L 87.929977 136.20316 \n",
       "L 89.149871 140.04001 \n",
       "L 89.759819 134.705855 \n",
       "L 90.979713 138.344652 \n",
       "L 91.58966 137.830921 \n",
       "L 92.199607 139.500006 \n",
       "L 92.809554 136.870449 \n",
       "L 93.419502 138.488941 \n",
       "L 94.639396 137.56042 \n",
       "L 95.249343 133.236011 \n",
       "L 95.85929 134.798827 \n",
       "L 96.469237 134.432311 \n",
       "L 97.689132 137.340003 \n",
       "L 98.299079 136.947286 \n",
       "L 98.909026 133.097154 \n",
       "L 99.518973 132.792644 \n",
       "L 100.12892 134.174497 \n",
       "L 101.348815 133.560002 \n",
       "L 101.958762 134.861325 \n",
       "L 102.568709 131.417423 \n",
       "L 104.398551 135.18 \n",
       "L 105.008498 134.885455 \n",
       "L 105.618445 136.050456 \n",
       "L 106.838339 141.096526 \n",
       "L 107.448286 137.957149 \n",
       "L 108.058234 140.382265 \n",
       "L 108.668181 140.04001 \n",
       "L 109.278128 141.038633 \n",
       "L 109.888075 140.696769 \n",
       "L 110.498022 141.660008 \n",
       "L 111.107969 141.318955 \n",
       "L 111.717917 142.249099 \n",
       "L 112.327864 140.66308 \n",
       "L 114.767652 148.930245 \n",
       "L 115.3776 149.701456 \n",
       "L 116.597494 148.902364 \n",
       "L 117.207441 149.646982 \n",
       "L 118.427335 153.294557 \n",
       "L 119.037283 151.780451 \n",
       "L 119.64723 153.540002 \n",
       "L 120.867124 154.831316 \n",
       "L 121.477071 152.320658 \n",
       "L 122.087018 152.96554 \n",
       "L 123.91686 148.808044 \n",
       "L 124.526807 149.462457 \n",
       "L 125.136754 151.085468 \n",
       "L 125.746701 151.704004 \n",
       "L 126.356649 153.272686 \n",
       "L 127.576543 150.656512 \n",
       "L 128.18649 151.255394 \n",
       "L 128.796437 152.768573 \n",
       "L 129.406384 150.585295 \n",
       "L 130.016332 152.076459 \n",
       "L 130.626279 149.040004 \n",
       "L 131.236226 148.734509 \n",
       "L 132.45612 151.642708 \n",
       "L 133.066067 150.454288 \n",
       "L 133.676015 151.007269 \n",
       "L 134.285962 150.697907 \n",
       "L 134.895909 151.239143 \n",
       "L 135.505856 148.41931 \n",
       "L 136.115803 147.309233 \n",
       "L 136.72575 147.0417 \n",
       "L 137.335698 148.412271 \n",
       "L 137.945645 148.950001 \n",
       "L 138.555592 150.282161 \n",
       "L 139.775486 149.720488 \n",
       "L 140.385433 151.014207 \n",
       "L 140.995381 150.732002 \n",
       "L 141.605328 151.225716 \n",
       "L 142.215275 150.180947 \n",
       "L 143.435169 149.646982 \n",
       "L 144.045116 148.638466 \n",
       "L 144.655064 149.871309 \n",
       "L 145.265011 150.349091 \n",
       "L 145.874958 151.550533 \n",
       "L 146.484905 152.008659 \n",
       "L 147.094852 151.020001 \n",
       "L 149.534641 152.801872 \n",
       "L 150.144588 152.537149 \n",
       "L 150.754535 152.96554 \n",
       "L 151.364482 152.703381 \n",
       "L 151.97443 153.804348 \n",
       "L 152.584377 152.865007 \n",
       "L 153.194324 153.949665 \n",
       "L 153.804271 154.353709 \n",
       "L 154.414218 154.091028 \n",
       "L 155.024165 153.175137 \n",
       "L 155.634113 152.923899 \n",
       "L 156.24406 152.02801 \n",
       "L 156.854007 151.787692 \n",
       "L 157.463954 152.190013 \n",
       "L 158.073901 151.951766 \n",
       "L 158.683848 152.3478 \n",
       "L 159.293796 153.365818 \n",
       "L 159.903743 153.124617 \n",
       "L 160.51369 153.505617 \n",
       "L 161.123637 152.651398 \n",
       "L 164.173373 151.519146 \n",
       "L 165.393267 153.441829 \n",
       "L 166.003214 152.629165 \n",
       "L 166.613162 152.408271 \n",
       "L 167.833056 153.124617 \n",
       "L 169.662897 150.777221 \n",
       "L 170.272845 151.136539 \n",
       "L 171.492739 150.732002 \n",
       "L 172.102686 149.980909 \n",
       "L 172.712633 149.787462 \n",
       "L 173.932528 148.321008 \n",
       "L 174.542475 148.680006 \n",
       "L 175.152422 147.960995 \n",
       "L 175.762369 147.783958 \n",
       "L 176.372316 147.077707 \n",
       "L 177.592211 146.738928 \n",
       "L 178.202158 146.049682 \n",
       "L 178.812105 145.887606 \n",
       "L 179.422052 146.244259 \n",
       "L 180.031999 147.11144 \n",
       "L 180.641946 147.457896 \n",
       "L 181.251894 147.291838 \n",
       "L 181.861841 146.621261 \n",
       "L 182.471788 145.454001 \n",
       "L 183.081735 145.801862 \n",
       "L 183.691682 145.647695 \n",
       "L 184.301629 144.999191 \n",
       "L 184.911577 145.344068 \n",
       "L 185.521524 144.703647 \n",
       "L 186.131471 145.046539 \n",
       "L 186.741418 144.900005 \n",
       "L 187.961312 145.573667 \n",
       "L 189.181207 147.187061 \n",
       "L 189.791154 146.08537 \n",
       "L 190.401101 146.409911 \n",
       "L 191.011048 146.261741 \n",
       "L 191.620995 146.582314 \n",
       "L 192.230943 145.504593 \n",
       "L 192.84089 145.362868 \n",
       "L 193.450837 143.840477 \n",
       "L 194.060784 144.624912 \n",
       "L 194.670731 144.032968 \n",
       "L 196.500573 143.640005 \n",
       "L 197.11052 142.615586 \n",
       "L 198.330414 142.370141 \n",
       "L 198.940361 141.807281 \n",
       "L 199.550309 140.369867 \n",
       "L 200.160256 139.821086 \n",
       "L 201.38015 140.473934 \n",
       "L 201.990097 140.364001 \n",
       "L 202.600044 141.115224 \n",
       "L 203.209992 141.003438 \n",
       "L 203.819939 140.46633 \n",
       "L 205.039833 141.096526 \n",
       "L 205.64978 141.828312 \n",
       "L 206.259727 141.296911 \n",
       "L 206.869675 142.021556 \n",
       "L 207.479622 141.909233 \n",
       "L 208.699516 143.334915 \n",
       "L 209.309463 143.628621 \n",
       "L 209.91941 143.103028 \n",
       "L 210.529358 143.801935 \n",
       "L 211.749252 143.569048 \n",
       "L 212.359199 142.249099 \n",
       "L 212.969146 142.540009 \n",
       "L 213.579093 143.226894 \n",
       "L 214.189041 143.511431 \n",
       "L 214.798988 144.188786 \n",
       "L 216.628829 143.846024 \n",
       "L 217.238776 143.344808 \n",
       "L 218.458671 143.897153 \n",
       "L 219.678565 143.675447 \n",
       "L 220.288512 143.947064 \n",
       "L 220.898459 143.457189 \n",
       "L 221.508407 142.592918 \n",
       "L 222.118354 142.865593 \n",
       "L 222.728301 142.385566 \n",
       "L 223.338248 142.656937 \n",
       "L 224.558142 143.935434 \n",
       "L 225.16809 144.197795 \n",
       "L 225.778037 143.721825 \n",
       "L 226.387984 143.616237 \n",
       "L 227.607878 142.679329 \n",
       "L 228.217825 141.853441 \n",
       "L 228.827773 142.479046 \n",
       "L 229.43772 142.380005 \n",
       "L 230.047667 142.640382 \n",
       "L 230.657614 143.256181 \n",
       "L 231.267561 142.443299 \n",
       "L 233.097403 143.209572 \n",
       "L 233.70735 143.1104 \n",
       "L 234.317297 143.711237 \n",
       "L 234.927244 143.610979 \n",
       "L 235.537191 144.205718 \n",
       "L 236.147139 143.758512 \n",
       "L 236.757086 143.659153 \n",
       "L 237.367033 143.90396 \n",
       "L 238.586927 143.706327 \n",
       "L 239.196874 143.948397 \n",
       "L 239.806822 144.527464 \n",
       "L 240.416769 144.765001 \n",
       "L 241.026716 144.664569 \n",
       "L 241.636663 144.22966 \n",
       "L 242.856557 145.36604 \n",
       "L 244.076452 144.503276 \n",
       "L 245.906293 144.212728 \n",
       "L 246.51624 144.769534 \n",
       "L 247.126188 144.347371 \n",
       "L 248.346082 144.803137 \n",
       "L 248.956029 145.3506 \n",
       "L 249.565976 145.252877 \n",
       "L 250.175923 144.516326 \n",
       "L 252.615712 144.142597 \n",
       "L 253.835606 144.586457 \n",
       "L 254.445554 144.181168 \n",
       "L 255.055501 144.401541 \n",
       "L 255.665448 144.931059 \n",
       "L 256.275395 144.528536 \n",
       "L 256.885342 144.437157 \n",
       "L 257.495289 143.731152 \n",
       "L 258.715184 144.166423 \n",
       "L 259.325131 144.077318 \n",
       "L 259.935078 144.292506 \n",
       "L 260.545025 144.20356 \n",
       "L 261.154972 144.718884 \n",
       "L 261.76492 144.930103 \n",
       "L 262.374867 145.44001 \n",
       "L 262.984814 145.647695 \n",
       "L 263.594761 145.555953 \n",
       "L 264.204708 145.762031 \n",
       "L 264.814655 145.374151 \n",
       "L 265.424603 145.284076 \n",
       "L 266.03455 144.900005 \n",
       "L 268.474338 144.550783 \n",
       "L 269.084286 144.754934 \n",
       "L 269.694233 144.668581 \n",
       "L 270.914127 145.072552 \n",
       "L 271.524074 144.699301 \n",
       "L 272.134021 144.614122 \n",
       "L 272.743969 145.099536 \n",
       "L 273.353916 144.729486 \n",
       "L 273.963863 143.794824 \n",
       "L 274.57381 143.713265 \n",
       "L 275.183757 144.195666 \n",
       "L 276.403652 144.03165 \n",
       "L 277.013599 144.22966 \n",
       "L 277.623546 143.312494 \n",
       "L 278.233493 143.233716 \n",
       "L 278.84344 143.43232 \n",
       "L 279.453387 143.353643 \n",
       "L 280.063335 143.000062 \n",
       "L 281.283229 143.394097 \n",
       "L 281.893176 143.316405 \n",
       "L 282.503123 142.966893 \n",
       "L 284.332965 142.740003 \n",
       "L 284.942912 142.934464 \n",
       "L 285.552859 142.590833 \n",
       "L 286.162806 142.516863 \n",
       "L 286.772753 142.977365 \n",
       "L 287.382701 143.169046 \n",
       "L 287.992648 143.625246 \n",
       "L 288.602595 143.549278 \n",
       "L 289.212542 143.737829 \n",
       "L 289.822489 143.398543 \n",
       "L 290.432436 142.798387 \n",
       "L 291.042384 142.987446 \n",
       "L 291.652331 143.436781 \n",
       "L 292.262278 143.101941 \n",
       "L 292.872225 143.028783 \n",
       "L 293.482172 143.47441 \n",
       "L 294.092119 143.659153 \n",
       "L 295.312014 142.99715 \n",
       "L 295.921961 142.412304 \n",
       "L 296.531908 142.342115 \n",
       "L 297.141855 141.762048 \n",
       "L 297.751802 142.202837 \n",
       "L 298.971697 142.57125 \n",
       "L 299.581644 143.006507 \n",
       "L 300.191591 142.935869 \n",
       "L 300.801538 142.363261 \n",
       "L 301.411485 142.795679 \n",
       "L 302.021433 142.726127 \n",
       "L 302.63138 142.906162 \n",
       "L 303.241327 143.333873 \n",
       "L 303.851274 143.015516 \n",
       "L 304.461221 142.451454 \n",
       "L 305.681116 141.824053 \n",
       "L 306.291063 142.00364 \n",
       "L 306.90101 142.427164 \n",
       "L 307.510957 142.11589 \n",
       "L 308.120904 142.049785 \n",
       "L 308.730851 142.227011 \n",
       "L 309.950746 142.095236 \n",
       "L 310.560693 141.78864 \n",
       "L 311.17064 141.724172 \n",
       "L 311.780587 141.900007 \n",
       "L 312.390534 142.314392 \n",
       "L 313.000482 142.249099 \n",
       "L 313.610429 141.945892 \n",
       "L 314.220376 142.35712 \n",
       "L 314.830323 142.05513 \n",
       "L 315.44027 141.991097 \n",
       "L 316.660165 142.334684 \n",
       "L 317.270112 142.270448 \n",
       "L 317.880059 141.972296 \n",
       "L 318.490006 141.909233 \n",
       "L 319.099953 141.613385 \n",
       "L 319.7099 141.551495 \n",
       "L 320.929795 140.965721 \n",
       "L 321.539742 140.905801 \n",
       "L 322.149689 141.306832 \n",
       "L 323.369583 141.186239 \n",
       "L 324.589478 141.523106 \n",
       "L 325.809372 141.402629 \n",
       "L 326.419319 141.569383 \n",
       "L 327.029266 141.509303 \n",
       "L 327.639214 141.675043 \n",
       "L 328.249161 141.615007 \n",
       "L 328.859108 141.779733 \n",
       "L 329.469055 142.167656 \n",
       "L 330.688949 142.492298 \n",
       "L 331.298897 142.875934 \n",
       "L 333.128738 142.690917 \n",
       "L 334.348632 143.4486 \n",
       "L 334.95858 143.166641 \n",
       "L 336.178474 143.480233 \n",
       "L 338.008315 143.294476 \n",
       "L 339.22821 143.604012 \n",
       "L 339.838157 143.326703 \n",
       "L 340.448104 143.480711 \n",
       "L 341.667998 143.35851 \n",
       "L 342.277946 143.511431 \n",
       "L 342.887893 143.450526 \n",
       "L 343.49784 143.602593 \n",
       "L 344.107787 143.329527 \n",
       "L 344.717734 143.269419 \n",
       "L 345.327681 143.420878 \n",
       "L 346.547576 142.880265 \n",
       "L 347.157523 142.821648 \n",
       "L 347.76747 142.972759 \n",
       "L 348.377417 143.332265 \n",
       "L 348.987365 143.273055 \n",
       "L 349.597312 143.422239 \n",
       "L 350.207259 143.363087 \n",
       "L 350.817206 143.09693 \n",
       "L 351.427153 143.038734 \n",
       "L 352.0371 142.568035 \n",
       "L 352.647048 142.923065 \n",
       "L 353.256995 142.660095 \n",
       "L 353.866942 142.603303 \n",
       "L 355.086836 142.898833 \n",
       "L 355.696783 143.249446 \n",
       "L 356.306731 143.395241 \n",
       "L 356.916678 143.743348 \n",
       "L 357.526625 143.887506 \n",
       "L 358.136572 143.626911 \n",
       "L 358.746519 143.972368 \n",
       "L 359.356466 143.511431 \n",
       "L 359.966414 143.45406 \n",
       "L 360.576361 143.797735 \n",
       "L 361.186308 143.940011 \n",
       "L 362.406202 143.824429 \n",
       "L 363.016149 143.965777 \n",
       "L 363.626097 143.709803 \n",
       "L 364.845991 143.991226 \n",
       "L 365.455938 143.933927 \n",
       "L 366.675832 144.212728 \n",
       "L 367.28578 143.959361 \n",
       "L 367.895727 143.902584 \n",
       "L 368.505674 144.236395 \n",
       "L 369.115621 144.374079 \n",
       "L 369.725568 144.122407 \n",
       "L 369.725568 144.122407 \n",
       "\" clip-path=\"url(#p5d83ec11e7)\" style=\"fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_14\">\n",
       "    <path d=\"M 65.361932 212.940003 \n",
       "L 65.971879 212.940003 \n",
       "L 66.581826 245.34 \n",
       "L 67.191773 237.240001 \n",
       "L 67.80172 193.500008 \n",
       "L 68.411668 212.940003 \n",
       "L 69.021615 171.282857 \n",
       "L 69.631562 176.490003 \n",
       "L 70.241509 169.74 \n",
       "L 71.461403 159.921823 \n",
       "L 72.071351 148.140002 \n",
       "L 73.291245 143.511431 \n",
       "L 73.901192 141.660008 \n",
       "L 75.121086 150.045884 \n",
       "L 75.731034 148.140002 \n",
       "L 76.950928 154.62001 \n",
       "L 77.560875 162.025715 \n",
       "L 78.170822 159.921823 \n",
       "L 78.780769 162.226969 \n",
       "L 79.390717 156.240009 \n",
       "L 80.000664 158.508003 \n",
       "L 80.610611 153.124617 \n",
       "L 81.220558 158.940001 \n",
       "L 81.830505 157.397144 \n",
       "L 82.440452 159.312426 \n",
       "L 83.0504 151.380013 \n",
       "L 84.270294 155.22751 \n",
       "L 84.880241 154.03092 \n",
       "L 85.490188 158.622354 \n",
       "L 86.100135 157.397144 \n",
       "L 86.710083 161.640008 \n",
       "L 87.32003 152.518392 \n",
       "L 88.539924 155.616924 \n",
       "L 89.149871 154.62001 \n",
       "L 89.759819 158.413177 \n",
       "L 90.369766 152.768573 \n",
       "L 90.979713 151.907446 \n",
       "L 91.58966 155.503646 \n",
       "L 92.199607 154.62001 \n",
       "L 92.809554 158.000878 \n",
       "L 94.029449 156.240009 \n",
       "L 94.639396 153.429808 \n",
       "L 95.249343 154.62001 \n",
       "L 95.85929 151.951766 \n",
       "L 96.469237 147.516932 \n",
       "L 97.689132 149.940007 \n",
       "L 98.299079 147.550912 \n",
       "L 99.518973 149.845267 \n",
       "L 101.958762 147.608862 \n",
       "L 102.568709 147.094842 \n",
       "L 104.398551 141.161544 \n",
       "L 105.008498 142.249099 \n",
       "L 105.618445 144.754934 \n",
       "L 106.228392 144.328238 \n",
       "L 106.838339 145.322617 \n",
       "L 107.448286 147.677154 \n",
       "L 108.058234 143.120293 \n",
       "L 108.668181 141.390014 \n",
       "L 109.278128 137.044111 \n",
       "L 109.888075 136.756228 \n",
       "L 110.498022 133.884007 \n",
       "L 111.107969 136.20316 \n",
       "L 111.717917 135.937408 \n",
       "L 112.327864 136.924619 \n",
       "L 113.547758 136.395014 \n",
       "L 114.767652 138.261963 \n",
       "L 115.987547 135.411439 \n",
       "L 116.597494 137.467071 \n",
       "L 117.207441 136.084189 \n",
       "L 117.817388 133.615867 \n",
       "L 119.037283 135.398433 \n",
       "L 119.64723 134.100006 \n",
       "L 120.257177 134.966377 \n",
       "L 120.867124 132.644357 \n",
       "L 121.477071 133.507744 \n",
       "L 122.087018 133.318729 \n",
       "L 122.696966 135.18 \n",
       "L 124.526807 134.584899 \n",
       "L 125.136754 135.376374 \n",
       "L 125.746701 137.124004 \n",
       "L 126.356649 137.874663 \n",
       "L 126.966596 139.563532 \n",
       "L 129.406384 142.332454 \n",
       "L 130.016332 139.358701 \n",
       "L 130.626279 138.240005 \n",
       "L 131.236226 139.817073 \n",
       "L 133.066067 141.775721 \n",
       "L 133.676015 140.685139 \n",
       "L 134.285962 140.46633 \n",
       "L 134.895909 138.560882 \n",
       "L 136.115803 141.493849 \n",
       "L 137.335698 141.061011 \n",
       "L 137.945645 142.470008 \n",
       "L 139.165539 142.031811 \n",
       "L 139.775486 143.398543 \n",
       "L 140.385433 143.959361 \n",
       "L 140.995381 143.7336 \n",
       "L 141.605328 144.28286 \n",
       "L 142.215275 145.588832 \n",
       "L 142.825222 145.355626 \n",
       "L 143.435169 143.619076 \n",
       "L 144.045116 144.900005 \n",
       "L 145.265011 145.930913 \n",
       "L 146.484905 145.480304 \n",
       "L 147.094852 145.980014 \n",
       "L 147.704799 145.757657 \n",
       "L 148.314747 146.248039 \n",
       "L 149.534641 145.809075 \n",
       "L 150.144588 146.982867 \n",
       "L 152.584377 148.815011 \n",
       "L 153.804271 148.361925 \n",
       "L 154.414218 147.478782 \n",
       "L 155.634113 144.443356 \n",
       "L 157.463954 145.795271 \n",
       "L 158.073901 146.869414 \n",
       "L 158.683848 147.298442 \n",
       "L 159.293796 148.349034 \n",
       "L 159.903743 148.140002 \n",
       "L 161.123637 150.190637 \n",
       "L 161.733584 148.751325 \n",
       "L 162.343531 149.152501 \n",
       "L 163.563426 148.740013 \n",
       "L 164.78332 149.522928 \n",
       "L 165.393267 149.318183 \n",
       "L 166.003214 149.701456 \n",
       "L 166.613162 150.662161 \n",
       "L 168.443003 151.761187 \n",
       "L 169.05295 152.687376 \n",
       "L 169.662897 153.037684 \n",
       "L 170.272845 153.945783 \n",
       "L 170.882792 153.167591 \n",
       "L 172.102686 153.846829 \n",
       "L 172.712633 153.631525 \n",
       "L 173.32258 152.872597 \n",
       "L 173.932528 152.665143 \n",
       "L 174.542475 153.000012 \n",
       "L 175.152422 152.794152 \n",
       "L 176.982263 153.774786 \n",
       "L 177.592211 154.62001 \n",
       "L 178.202158 154.933558 \n",
       "L 178.812105 153.684392 \n",
       "L 180.031999 153.282868 \n",
       "L 180.641946 152.573692 \n",
       "L 181.251894 152.889746 \n",
       "L 181.861841 152.190013 \n",
       "L 182.471788 152.001142 \n",
       "L 183.081735 152.31527 \n",
       "L 183.691682 153.124617 \n",
       "L 184.301629 151.942048 \n",
       "L 185.521524 152.558194 \n",
       "L 186.131471 151.884735 \n",
       "L 186.741418 150.246009 \n",
       "L 187.351365 150.55792 \n",
       "L 187.961312 151.347931 \n",
       "L 189.181207 151.951766 \n",
       "L 189.791154 152.723427 \n",
       "L 190.401101 153.015741 \n",
       "L 191.011048 151.896525 \n",
       "L 191.620995 152.190013 \n",
       "L 192.230943 152.945755 \n",
       "L 192.84089 153.231436 \n",
       "L 193.450837 152.132424 \n",
       "L 194.060784 151.502272 \n",
       "L 194.670731 151.790705 \n",
       "L 195.280678 152.53066 \n",
       "L 195.890626 151.907446 \n",
       "L 196.500573 151.740011 \n",
       "L 197.11052 151.126183 \n",
       "L 197.720467 151.409734 \n",
       "L 198.330414 152.134525 \n",
       "L 199.550309 152.684798 \n",
       "L 200.160256 153.394061 \n",
       "L 201.38015 152.190013 \n",
       "L 201.990097 152.460007 \n",
       "L 202.600044 152.297527 \n",
       "L 204.429886 153.09197 \n",
       "L 205.039833 152.929576 \n",
       "L 205.64978 151.927013 \n",
       "L 206.259727 152.608975 \n",
       "L 208.089569 153.379158 \n",
       "L 209.309463 153.061525 \n",
       "L 209.91941 153.313111 \n",
       "L 211.139305 152.190013 \n",
       "L 212.359199 152.692069 \n",
       "L 212.969146 152.14 \n",
       "L 213.579093 152.389181 \n",
       "L 214.798988 152.091232 \n",
       "L 215.408935 152.337575 \n",
       "L 216.018882 152.973883 \n",
       "L 216.628829 152.43398 \n",
       "L 218.458671 153.154295 \n",
       "L 219.678565 152.094332 \n",
       "L 220.288512 152.714128 \n",
       "L 220.898459 152.949376 \n",
       "L 221.508407 153.561018 \n",
       "L 222.728301 154.01955 \n",
       "L 223.338248 153.872321 \n",
       "L 223.948195 154.098632 \n",
       "L 224.558142 154.694211 \n",
       "L 225.778037 153.662738 \n",
       "L 226.387984 153.886428 \n",
       "L 226.997931 153.377608 \n",
       "L 227.607878 153.600675 \n",
       "L 228.217825 154.184783 \n",
       "L 230.047667 152.683176 \n",
       "L 231.877508 153.342933 \n",
       "L 232.487456 153.20619 \n",
       "L 233.097403 152.71827 \n",
       "L 233.70735 152.584772 \n",
       "L 234.317297 153.151514 \n",
       "L 235.537191 152.190013 \n",
       "L 236.147139 152.4062 \n",
       "L 236.757086 151.931489 \n",
       "L 238.586927 151.550533 \n",
       "L 239.806822 151.97833 \n",
       "L 240.416769 151.515004 \n",
       "L 242.24661 151.146199 \n",
       "L 242.856557 151.357809 \n",
       "L 243.466505 150.904506 \n",
       "L 244.076452 151.115522 \n",
       "L 245.296346 150.219735 \n",
       "L 245.906293 150.103646 \n",
       "L 248.346082 148.355291 \n",
       "L 248.956029 147.60359 \n",
       "L 250.175923 147.393949 \n",
       "L 250.785871 146.971482 \n",
       "L 251.395818 146.869414 \n",
       "L 252.005765 147.084631 \n",
       "L 252.615712 146.667276 \n",
       "L 253.225659 146.567192 \n",
       "L 253.835606 147.094842 \n",
       "L 254.445554 147.306568 \n",
       "L 256.275395 147.004969 \n",
       "L 256.885342 147.214291 \n",
       "L 257.495289 147.729875 \n",
       "L 258.105237 147.628966 \n",
       "L 258.715184 147.223025 \n",
       "L 259.325131 146.210221 \n",
       "L 259.935078 146.115004 \n",
       "L 260.545025 146.625983 \n",
       "L 261.154972 146.83193 \n",
       "L 261.76492 146.735669 \n",
       "L 262.374867 146.340012 \n",
       "L 263.594761 146.748589 \n",
       "L 264.204708 146.653763 \n",
       "L 264.814655 146.855857 \n",
       "L 265.424603 146.761277 \n",
       "L 266.03455 147.256367 \n",
       "L 266.644497 147.454811 \n",
       "L 267.254444 147.359289 \n",
       "L 267.864391 147.848122 \n",
       "L 268.474338 147.460967 \n",
       "L 269.084286 147.946569 \n",
       "L 270.30418 147.755439 \n",
       "L 272.743969 148.52006 \n",
       "L 273.353916 148.42422 \n",
       "L 273.963863 148.612308 \n",
       "L 275.183757 148.421743 \n",
       "L 276.403652 147.673142 \n",
       "L 277.013599 147.860694 \n",
       "L 277.623546 147.768663 \n",
       "L 278.233493 147.121724 \n",
       "L 280.063335 147.681079 \n",
       "L 281.283229 147.50113 \n",
       "L 281.893176 146.865851 \n",
       "L 282.503123 146.506389 \n",
       "L 283.11307 146.963473 \n",
       "L 283.723018 146.876497 \n",
       "L 284.332965 147.330003 \n",
       "L 284.942912 146.703993 \n",
       "L 285.552859 146.618465 \n",
       "L 286.772753 146.982867 \n",
       "L 287.382701 146.897267 \n",
       "L 287.992648 146.28099 \n",
       "L 289.822489 145.242449 \n",
       "L 290.432436 145.42541 \n",
       "L 291.042384 144.821415 \n",
       "L 291.652331 144.743231 \n",
       "L 292.262278 145.186657 \n",
       "L 292.872225 145.367822 \n",
       "L 293.482172 145.807206 \n",
       "L 294.702067 145.647695 \n",
       "L 295.312014 145.054288 \n",
       "L 297.141855 144.823472 \n",
       "L 297.751802 144.238437 \n",
       "L 300.801538 145.126056 \n",
       "L 301.411485 145.551348 \n",
       "L 302.021433 145.72459 \n",
       "L 302.63138 145.647695 \n",
       "L 303.241327 145.322617 \n",
       "L 306.291063 146.176372 \n",
       "L 306.90101 146.099709 \n",
       "L 307.510957 145.779209 \n",
       "L 308.120904 145.947526 \n",
       "L 308.730851 145.62901 \n",
       "L 311.17064 146.295459 \n",
       "L 311.780587 145.740001 \n",
       "L 312.390534 145.666118 \n",
       "L 313.000482 145.831409 \n",
       "L 313.610429 145.757657 \n",
       "L 314.220376 145.208962 \n",
       "L 316.050217 145.70214 \n",
       "L 316.660165 145.158891 \n",
       "L 317.880059 145.953986 \n",
       "L 318.490006 146.115004 \n",
       "L 319.099953 146.042164 \n",
       "L 319.7099 146.202212 \n",
       "L 320.319848 146.129502 \n",
       "L 321.539742 146.446889 \n",
       "L 322.759636 146.301702 \n",
       "L 323.369583 146.688119 \n",
       "L 324.589478 146.086485 \n",
       "L 325.199425 146.470686 \n",
       "L 325.809372 146.171781 \n",
       "L 327.029266 146.030244 \n",
       "L 327.639214 145.50891 \n",
       "L 328.249161 145.215002 \n",
       "L 328.859108 145.146942 \n",
       "L 329.469055 145.527101 \n",
       "L 330.688949 145.39046 \n",
       "L 331.298897 145.545047 \n",
       "L 332.518791 146.294909 \n",
       "L 333.128738 146.446367 \n",
       "L 334.95858 146.238422 \n",
       "L 336.178474 146.53821 \n",
       "L 336.788421 146.90503 \n",
       "L 337.398368 146.835304 \n",
       "L 338.618263 147.562731 \n",
       "L 339.838157 147.421599 \n",
       "L 340.448104 147.136469 \n",
       "L 341.058051 147.281728 \n",
       "L 341.667998 147.640451 \n",
       "L 342.277946 147.783958 \n",
       "L 342.887893 147.500537 \n",
       "L 343.49784 146.792968 \n",
       "L 345.327681 145.956535 \n",
       "L 345.937629 145.890981 \n",
       "L 346.547576 146.246504 \n",
       "L 347.76747 146.533966 \n",
       "L 348.377417 146.049682 \n",
       "L 348.987365 145.776066 \n",
       "L 350.207259 145.647695 \n",
       "L 350.817206 145.791187 \n",
       "L 351.427153 145.72724 \n",
       "L 353.256995 146.770025 \n",
       "L 353.866942 146.499494 \n",
       "L 354.476889 146.63938 \n",
       "L 355.086836 146.574463 \n",
       "L 355.696783 146.306047 \n",
       "L 356.306731 146.648795 \n",
       "L 356.916678 146.584269 \n",
       "L 357.526625 146.722503 \n",
       "L 358.136572 147.062253 \n",
       "L 358.746519 146.392284 \n",
       "L 359.356466 146.32883 \n",
       "L 359.966414 146.667276 \n",
       "L 360.576361 146.803918 \n",
       "L 361.186308 146.340012 \n",
       "L 361.796255 146.676358 \n",
       "L 363.626097 147.082053 \n",
       "L 364.236044 147.018222 \n",
       "L 364.845991 147.349759 \n",
       "L 365.455938 147.482808 \n",
       "L 366.065885 147.221793 \n",
       "L 366.675832 147.158195 \n",
       "L 367.28578 146.898874 \n",
       "L 367.895727 147.031764 \n",
       "L 368.505674 146.578562 \n",
       "L 369.115621 146.906333 \n",
       "L 369.725568 146.844009 \n",
       "L 369.725568 146.844009 \n",
       "\" clip-path=\"url(#p5d83ec11e7)\" style=\"fill: none; stroke: #2ca02c; stroke-width: 1.5; stroke-linecap: square\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_15\">\n",
       "    <path d=\"M 65.361932 18.54 \n",
       "L 65.971879 115.740005 \n",
       "L 66.581826 148.140002 \n",
       "L 67.191773 140.04001 \n",
       "L 67.80172 154.62001 \n",
       "L 68.411668 164.340001 \n",
       "L 69.021615 157.397144 \n",
       "L 69.631562 152.190013 \n",
       "L 70.241509 148.140002 \n",
       "L 70.851456 144.900005 \n",
       "L 71.461403 159.921823 \n",
       "L 72.681298 168.078462 \n",
       "L 73.291245 157.397144 \n",
       "L 73.901192 161.100004 \n",
       "L 75.121086 155.763531 \n",
       "L 75.731034 158.940001 \n",
       "L 76.340981 146.434737 \n",
       "L 76.950928 140.04001 \n",
       "L 77.560875 143.511431 \n",
       "L 78.170822 142.249099 \n",
       "L 78.780769 132.644357 \n",
       "L 79.390717 135.990014 \n",
       "L 80.000664 142.956001 \n",
       "L 80.610611 141.909233 \n",
       "L 81.220558 144.540007 \n",
       "L 81.830505 140.04001 \n",
       "L 83.0504 144.900005 \n",
       "L 83.660347 140.82388 \n",
       "L 84.270294 143.077507 \n",
       "L 85.490188 135.751768 \n",
       "L 86.100135 137.957149 \n",
       "L 86.710083 142.740003 \n",
       "L 87.32003 139.383251 \n",
       "L 87.929977 143.876846 \n",
       "L 89.149871 142.470008 \n",
       "L 89.759819 144.188786 \n",
       "L 90.369766 148.140002 \n",
       "L 90.979713 147.386519 \n",
       "L 91.58966 140.04001 \n",
       "L 92.809554 143.209572 \n",
       "L 93.419502 146.761277 \n",
       "L 94.029449 142.065008 \n",
       "L 94.639396 143.511431 \n",
       "L 95.249343 142.956001 \n",
       "L 95.85929 138.610591 \n",
       "L 97.079185 137.747552 \n",
       "L 98.299079 140.481828 \n",
       "L 98.909026 143.511431 \n",
       "L 99.518973 143.024221 \n",
       "L 100.12892 140.877934 \n",
       "L 100.738868 143.74678 \n",
       "L 101.348815 143.280007 \n",
       "L 103.788603 147.63376 \n",
       "L 104.398551 147.143088 \n",
       "L 105.008498 143.721825 \n",
       "L 105.618445 143.304181 \n",
       "L 106.838339 139.687833 \n",
       "L 107.448286 142.122871 \n",
       "L 108.058234 141.751272 \n",
       "L 109.278128 143.701649 \n",
       "L 109.888075 143.323792 \n",
       "L 110.498022 141.660008 \n",
       "L 111.107969 141.318955 \n",
       "L 112.937811 144.038747 \n",
       "L 113.547758 143.685006 \n",
       "L 114.767652 145.374151 \n",
       "L 116.597494 140.897661 \n",
       "L 117.207441 142.865593 \n",
       "L 117.817388 143.671044 \n",
       "L 118.427335 143.353643 \n",
       "L 119.037283 144.135515 \n",
       "L 119.64723 142.740003 \n",
       "L 120.257177 143.511431 \n",
       "L 120.867124 145.322617 \n",
       "L 121.477071 146.049682 \n",
       "L 122.087018 144.693204 \n",
       "L 122.696966 145.411592 \n",
       "L 123.306913 147.127503 \n",
       "L 123.91686 146.803918 \n",
       "L 124.526807 147.478782 \n",
       "L 125.136754 147.158195 \n",
       "L 125.746701 144.900005 \n",
       "L 126.356649 144.611297 \n",
       "L 126.966596 146.23412 \n",
       "L 127.576543 145.938068 \n",
       "L 128.18649 146.582314 \n",
       "L 128.796437 144.437157 \n",
       "L 129.406384 145.083401 \n",
       "L 130.016332 146.625983 \n",
       "L 130.626279 147.24 \n",
       "L 131.236226 146.951016 \n",
       "L 131.846173 144.900005 \n",
       "L 133.066067 146.115004 \n",
       "L 133.676015 144.986025 \n",
       "L 134.285962 145.582111 \n",
       "L 134.895909 145.322617 \n",
       "L 137.335698 147.595464 \n",
       "L 137.945645 146.520004 \n",
       "L 138.555592 147.872238 \n",
       "L 139.165539 148.405579 \n",
       "L 139.775486 147.349759 \n",
       "L 140.385433 145.527101 \n",
       "L 140.995381 144.511213 \n",
       "L 141.605328 144.28286 \n",
       "L 142.215275 144.823472 \n",
       "L 142.825222 146.115004 \n",
       "L 144.045116 147.143088 \n",
       "L 144.655064 146.903364 \n",
       "L 145.265011 145.930913 \n",
       "L 145.874958 146.434737 \n",
       "L 146.484905 146.205673 \n",
       "L 147.704799 147.187061 \n",
       "L 148.314747 146.248039 \n",
       "L 149.534641 148.606196 \n",
       "L 150.144588 149.065728 \n",
       "L 151.364482 147.227326 \n",
       "L 151.97443 148.366574 \n",
       "L 152.584377 147.465008 \n",
       "L 153.194324 147.916559 \n",
       "L 153.804271 147.696171 \n",
       "L 154.414218 148.140002 \n",
       "L 156.854007 152.431402 \n",
       "L 158.073901 153.222355 \n",
       "L 159.293796 151.484529 \n",
       "L 159.903743 151.878463 \n",
       "L 161.123637 151.421017 \n",
       "L 161.733584 150.585295 \n",
       "L 162.343531 150.3675 \n",
       "L 162.953479 151.359881 \n",
       "L 163.563426 151.14 \n",
       "L 164.173373 152.115464 \n",
       "L 165.393267 152.852739 \n",
       "L 166.003214 153.800249 \n",
       "L 167.223109 153.347148 \n",
       "L 167.833056 154.274916 \n",
       "L 169.05295 153.82422 \n",
       "L 169.662897 154.733028 \n",
       "L 170.272845 153.945783 \n",
       "L 170.882792 153.726207 \n",
       "L 171.492739 154.06458 \n",
       "L 172.102686 154.951373 \n",
       "L 172.712633 155.278985 \n",
       "L 173.32258 156.148992 \n",
       "L 173.932528 156.466262 \n",
       "L 175.762369 154.192749 \n",
       "L 176.372316 155.044925 \n",
       "L 176.982263 155.359574 \n",
       "L 177.592211 154.094606 \n",
       "L 178.202158 153.888398 \n",
       "L 178.812105 154.204177 \n",
       "L 179.422052 153.999577 \n",
       "L 184.301629 156.405314 \n",
       "L 184.911577 155.705494 \n",
       "L 185.521524 156.485468 \n",
       "L 186.131471 156.76915 \n",
       "L 186.741418 157.536001 \n",
       "L 187.351365 157.811645 \n",
       "L 187.961312 157.603366 \n",
       "L 189.181207 155.287067 \n",
       "L 189.791154 154.62001 \n",
       "L 190.401101 153.487584 \n",
       "L 191.620995 154.059236 \n",
       "L 192.230943 154.806042 \n",
       "L 192.84089 154.62001 \n",
       "L 193.450837 155.357068 \n",
       "L 194.060784 155.170197 \n",
       "L 194.670731 155.897753 \n",
       "L 195.280678 154.801682 \n",
       "L 195.890626 154.62001 \n",
       "L 198.940361 155.945463 \n",
       "L 199.550309 156.643169 \n",
       "L 200.770203 157.148078 \n",
       "L 201.990097 158.508003 \n",
       "L 202.600044 157.458585 \n",
       "L 203.209992 157.703001 \n",
       "L 204.429886 157.336514 \n",
       "L 205.039833 158.000878 \n",
       "L 205.64978 158.238704 \n",
       "L 206.259727 158.89345 \n",
       "L 206.869675 158.291078 \n",
       "L 207.479622 158.109232 \n",
       "L 208.699516 156.926445 \n",
       "L 209.309463 157.162794 \n",
       "L 209.91941 156.580337 \n",
       "L 210.529358 156.409456 \n",
       "L 212.359199 157.110261 \n",
       "L 212.969146 157.740008 \n",
       "L 213.579093 157.567881 \n",
       "L 214.798988 156.437569 \n",
       "L 215.408935 157.059842 \n",
       "L 216.018882 156.501299 \n",
       "L 216.628829 156.337601 \n",
       "L 217.238776 156.564 \n",
       "L 217.848724 157.175859 \n",
       "L 218.458671 156.625716 \n",
       "L 219.068618 157.232491 \n",
       "L 219.678565 157.069141 \n",
       "L 220.288512 157.288239 \n",
       "L 220.898459 157.125947 \n",
       "L 222.118354 156.051631 \n",
       "L 223.338248 156.489233 \n",
       "L 225.16809 156.024415 \n",
       "L 225.778037 156.240009 \n",
       "L 226.387984 155.353592 \n",
       "L 226.997931 155.204668 \n",
       "L 227.607878 155.784952 \n",
       "L 228.217825 155.635522 \n",
       "L 228.827773 155.848551 \n",
       "L 229.43772 155.340006 \n",
       "L 230.047667 155.911223 \n",
       "L 230.657614 156.120893 \n",
       "L 231.267561 156.685056 \n",
       "L 231.877508 156.890366 \n",
       "L 232.487456 156.387281 \n",
       "L 233.097403 156.240009 \n",
       "L 233.70735 156.444695 \n",
       "L 234.317297 155.948635 \n",
       "L 234.927244 156.501299 \n",
       "L 235.537191 155.661434 \n",
       "L 236.147139 155.86528 \n",
       "L 236.757086 156.412353 \n",
       "L 237.367033 156.268629 \n",
       "L 237.97698 156.468174 \n",
       "L 238.586927 157.007382 \n",
       "L 239.196874 155.16378 \n",
       "L 239.806822 155.026415 \n",
       "L 240.416769 155.565 \n",
       "L 241.636663 154.62001 \n",
       "L 244.076452 154.091028 \n",
       "L 245.296346 155.145415 \n",
       "L 245.906293 155.340006 \n",
       "L 246.51624 155.207116 \n",
       "L 247.126188 155.400201 \n",
       "L 248.346082 154.490842 \n",
       "L 248.956029 155.006239 \n",
       "L 249.565976 154.876636 \n",
       "L 250.175923 154.428171 \n",
       "L 250.785871 154.62001 \n",
       "L 251.395818 155.128237 \n",
       "L 252.005765 154.683334 \n",
       "L 253.225659 154.43127 \n",
       "L 253.835606 153.992914 \n",
       "L 254.445554 154.494985 \n",
       "L 255.055501 154.059236 \n",
       "L 256.275395 154.434268 \n",
       "L 256.885342 154.928576 \n",
       "L 258.715184 155.475851 \n",
       "L 259.325131 155.9607 \n",
       "L 259.935078 156.138751 \n",
       "L 260.545025 156.012901 \n",
       "L 262.984814 154.320932 \n",
       "L 264.204708 154.679452 \n",
       "L 265.424603 155.6245 \n",
       "L 266.03455 155.2091 \n",
       "L 267.254444 155.556874 \n",
       "L 269.084286 155.200309 \n",
       "L 270.914127 155.712794 \n",
       "L 271.524074 155.021418 \n",
       "L 272.134021 154.905894 \n",
       "L 272.743969 153.935905 \n",
       "L 273.963863 154.846713 \n",
       "L 276.403652 154.395915 \n",
       "L 277.013599 153.726207 \n",
       "L 277.623546 153.895886 \n",
       "L 278.84344 153.678468 \n",
       "L 279.453387 153.846829 \n",
       "L 280.063335 154.289588 \n",
       "L 280.673282 153.631525 \n",
       "L 281.893176 153.418655 \n",
       "L 282.503123 153.58538 \n",
       "L 283.11307 153.20816 \n",
       "L 283.723018 153.374552 \n",
       "L 284.332965 153.000012 \n",
       "L 284.942912 153.435297 \n",
       "L 285.552859 153.331172 \n",
       "L 286.162806 153.763141 \n",
       "L 286.772753 153.658683 \n",
       "L 287.382701 153.821106 \n",
       "L 287.992648 154.248208 \n",
       "L 288.602595 153.878433 \n",
       "L 289.212542 153.774786 \n",
       "L 289.822489 153.935123 \n",
       "L 291.652331 152.843238 \n",
       "L 292.262278 153.264937 \n",
       "L 292.872225 153.424492 \n",
       "L 294.092119 153.224049 \n",
       "L 295.312014 154.054297 \n",
       "L 295.921961 154.209666 \n",
       "L 296.531908 154.108423 \n",
       "L 297.751802 154.416453 \n",
       "L 298.36175 154.315457 \n",
       "L 298.971697 153.961875 \n",
       "L 299.581644 153.357663 \n",
       "L 300.191591 153.008398 \n",
       "L 300.801538 153.414426 \n",
       "L 301.411485 153.317326 \n",
       "L 302.021433 153.470595 \n",
       "L 302.63138 153.124617 \n",
       "L 303.241327 153.029009 \n",
       "L 303.851274 153.429808 \n",
       "L 304.461221 153.581223 \n",
       "L 305.071168 153.48518 \n",
       "L 305.681116 153.881779 \n",
       "L 306.90101 154.179308 \n",
       "L 307.510957 154.571156 \n",
       "L 308.120904 154.717444 \n",
       "L 308.730851 154.62001 \n",
       "L 309.340799 154.280652 \n",
       "L 309.950746 154.426577 \n",
       "L 310.560693 154.812965 \n",
       "L 311.17064 154.956834 \n",
       "L 311.780587 154.860009 \n",
       "L 313.000482 155.145415 \n",
       "L 313.610429 154.81059 \n",
       "L 314.220376 154.95272 \n",
       "L 314.830323 154.62001 \n",
       "L 315.44027 154.998403 \n",
       "L 316.050217 154.903113 \n",
       "L 316.660165 155.043636 \n",
       "L 317.270112 154.948708 \n",
       "L 318.490006 155.22751 \n",
       "L 320.319848 154.944783 \n",
       "L 320.929795 154.388571 \n",
       "L 323.369583 154.023968 \n",
       "L 323.979531 154.391294 \n",
       "L 324.589478 154.072402 \n",
       "L 325.199425 154.437904 \n",
       "L 325.809372 154.574589 \n",
       "L 327.029266 154.393959 \n",
       "L 327.639214 154.755319 \n",
       "L 328.249161 154.890005 \n",
       "L 328.859108 155.248555 \n",
       "L 329.469055 154.933558 \n",
       "L 330.079002 154.843454 \n",
       "L 330.688949 154.530833 \n",
       "L 331.298897 154.442061 \n",
       "L 331.908844 154.575617 \n",
       "L 332.518791 154.044332 \n",
       "L 333.128738 153.957284 \n",
       "L 333.738685 153.65021 \n",
       "L 334.348632 153.124617 \n",
       "L 334.95858 152.820817 \n",
       "L 336.178474 152.654165 \n",
       "L 337.398368 153.358793 \n",
       "L 338.008315 153.27483 \n",
       "L 339.22821 153.540002 \n",
       "L 339.838157 153.240677 \n",
       "L 340.448104 153.372756 \n",
       "L 341.058051 153.075111 \n",
       "L 341.667998 152.992871 \n",
       "L 342.277946 152.69737 \n",
       "L 342.887893 152.829478 \n",
       "L 343.49784 153.173703 \n",
       "L 344.107787 153.304203 \n",
       "L 344.717734 153.222355 \n",
       "L 345.327681 153.56348 \n",
       "L 345.937629 153.692286 \n",
       "L 346.547576 152.978967 \n",
       "L 347.157523 153.318412 \n",
       "L 347.76747 153.237418 \n",
       "L 348.377417 152.738722 \n",
       "L 348.987365 152.659321 \n",
       "L 349.597312 152.163985 \n",
       "L 350.207259 152.293848 \n",
       "L 352.0371 152.061019 \n",
       "L 352.647048 151.778148 \n",
       "L 353.866942 152.446335 \n",
       "L 355.696783 152.826798 \n",
       "L 356.306731 152.545868 \n",
       "L 356.916678 151.860257 \n",
       "L 358.746519 152.240417 \n",
       "L 359.356466 152.567333 \n",
       "L 359.966414 152.491249 \n",
       "L 361.186308 152.740011 \n",
       "L 361.796255 152.264851 \n",
       "L 363.016149 152.513019 \n",
       "L 363.626097 152.437963 \n",
       "L 365.455938 152.80613 \n",
       "L 366.065885 153.124617 \n",
       "L 367.28578 153.365818 \n",
       "L 368.505674 153.214707 \n",
       "L 369.115621 153.529182 \n",
       "L 369.725568 153.648008 \n",
       "L 369.725568 153.648008 \n",
       "\" clip-path=\"url(#p5d83ec11e7)\" style=\"fill: none; stroke: #d62728; stroke-width: 1.5; stroke-linecap: square\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_16\">\n",
       "    <path d=\"M 65.361932 115.740005 \n",
       "L 65.971879 67.14001 \n",
       "L 66.581826 115.740005 \n",
       "L 67.191773 140.04001 \n",
       "L 67.80172 154.62001 \n",
       "L 68.411668 131.940004 \n",
       "L 69.021615 157.397144 \n",
       "L 69.631562 164.340001 \n",
       "L 70.241509 137.340003 \n",
       "L 70.851456 154.62001 \n",
       "L 71.461403 151.085468 \n",
       "L 72.681298 160.601539 \n",
       "L 73.901192 167.580012 \n",
       "L 75.121086 184.351763 \n",
       "L 75.731034 175.139999 \n",
       "L 76.340981 177.129483 \n",
       "L 76.950928 183.78001 \n",
       "L 77.560875 175.911428 \n",
       "L 78.170822 173.17637 \n",
       "L 78.780769 179.131307 \n",
       "L 79.390717 176.490003 \n",
       "L 80.000664 170.172012 \n",
       "L 81.220558 180.539999 \n",
       "L 81.830505 174.754292 \n",
       "L 82.440452 166.015863 \n",
       "L 83.0504 161.100004 \n",
       "L 84.270294 170.415009 \n",
       "L 84.880241 171.703644 \n",
       "L 85.490188 175.775294 \n",
       "L 86.100135 171.282857 \n",
       "L 86.710083 172.440007 \n",
       "L 87.32003 176.161623 \n",
       "L 87.929977 172.013687 \n",
       "L 88.539924 175.555384 \n",
       "L 89.149871 176.490003 \n",
       "L 89.759819 172.637568 \n",
       "L 90.369766 173.597142 \n",
       "L 90.979713 172.251629 \n",
       "L 91.58966 175.385459 \n",
       "L 92.199607 176.220008 \n",
       "L 92.809554 172.792184 \n",
       "L 93.419502 171.5783 \n",
       "L 94.029449 172.440007 \n",
       "L 94.639396 175.250208 \n",
       "L 95.85929 176.728235 \n",
       "L 97.689132 173.340009 \n",
       "L 98.299079 174.060005 \n",
       "L 98.909026 173.018582 \n",
       "L 99.518973 173.718952 \n",
       "L 100.12892 176.071041 \n",
       "L 100.738868 175.048476 \n",
       "L 101.348815 175.680004 \n",
       "L 101.958762 177.884269 \n",
       "L 104.398551 174.060005 \n",
       "L 105.008498 176.121822 \n",
       "L 105.618445 172.31911 \n",
       "L 106.228392 170.057647 \n",
       "L 106.838339 170.679138 \n",
       "L 107.448286 167.117149 \n",
       "L 108.058234 167.762538 \n",
       "L 108.668181 165.690004 \n",
       "L 109.888075 169.59406 \n",
       "L 110.498022 170.172012 \n",
       "L 111.107969 166.897906 \n",
       "L 111.717917 166.233513 \n",
       "L 112.327864 164.340001 \n",
       "L 112.937811 161.264063 \n",
       "L 113.547758 161.910003 \n",
       "L 114.157705 163.740004 \n",
       "L 114.767652 161.969271 \n",
       "L 115.987547 163.182865 \n",
       "L 117.207441 162.079537 \n",
       "L 117.817388 162.664138 \n",
       "L 118.427335 161.026367 \n",
       "L 119.037283 160.517533 \n",
       "L 119.64723 161.100004 \n",
       "L 120.257177 160.601539 \n",
       "L 120.867124 159.057393 \n",
       "L 121.477071 158.591619 \n",
       "L 122.087018 157.101715 \n",
       "L 122.696966 157.689473 \n",
       "L 123.306913 157.252508 \n",
       "L 123.91686 157.826607 \n",
       "L 126.966596 150.998825 \n",
       "L 127.576543 151.600198 \n",
       "L 128.18649 151.255394 \n",
       "L 128.796437 149.991439 \n",
       "L 129.406384 150.585295 \n",
       "L 130.016332 150.259638 \n",
       "L 131.236226 151.409734 \n",
       "L 131.846173 149.318183 \n",
       "L 133.066067 148.718577 \n",
       "L 133.676015 150.147083 \n",
       "L 134.285962 149.845267 \n",
       "L 134.895909 151.239143 \n",
       "L 136.72575 152.80781 \n",
       "L 138.555592 149.478853 \n",
       "L 140.995381 151.509601 \n",
       "L 141.605328 151.225716 \n",
       "L 142.215275 152.477012 \n",
       "L 142.825222 152.949376 \n",
       "L 143.435169 152.660943 \n",
       "L 144.045116 150.881549 \n",
       "L 144.655064 149.871309 \n",
       "L 145.265011 151.085468 \n",
       "L 145.874958 150.088873 \n",
       "L 146.484905 150.55792 \n",
       "L 148.314747 149.795486 \n",
       "L 148.924694 148.140002 \n",
       "L 149.534641 148.606196 \n",
       "L 150.144588 146.982867 \n",
       "L 150.754535 146.761277 \n",
       "L 151.364482 147.911837 \n",
       "L 151.97443 148.366574 \n",
       "L 153.194324 147.916559 \n",
       "L 153.804271 148.361925 \n",
       "L 154.414218 148.140002 \n",
       "L 155.024165 148.577851 \n",
       "L 155.634113 149.662162 \n",
       "L 156.24406 148.788013 \n",
       "L 156.854007 148.569146 \n",
       "L 157.463954 148.992642 \n",
       "L 158.073901 148.140002 \n",
       "L 159.293796 147.721938 \n",
       "L 160.51369 148.552751 \n",
       "L 161.123637 147.729875 \n",
       "L 162.343531 148.545002 \n",
       "L 162.953479 149.548709 \n",
       "L 163.563426 149.940007 \n",
       "L 164.173373 148.537557 \n",
       "L 164.78332 148.930245 \n",
       "L 165.393267 147.550912 \n",
       "L 166.003214 147.359289 \n",
       "L 166.613162 146.587904 \n",
       "L 167.223109 145.247156 \n",
       "L 167.833056 145.072552 \n",
       "L 169.662897 146.25628 \n",
       "L 170.272845 146.079895 \n",
       "L 172.712633 147.590858 \n",
       "L 173.32258 146.865851 \n",
       "L 173.932528 147.234974 \n",
       "L 174.542475 147.060008 \n",
       "L 175.152422 147.423989 \n",
       "L 176.372316 149.202297 \n",
       "L 176.982263 148.492179 \n",
       "L 177.592211 148.840546 \n",
       "L 178.812105 150.565669 \n",
       "L 179.422052 150.380434 \n",
       "L 180.641946 151.03896 \n",
       "L 181.861841 150.671257 \n",
       "L 182.471788 151.497521 \n",
       "L 183.081735 150.311143 \n",
       "L 183.691682 150.13386 \n",
       "L 184.301629 150.950217 \n",
       "L 185.521524 150.59455 \n",
       "L 186.131471 149.930969 \n",
       "L 186.741418 150.246009 \n",
       "L 187.351365 150.074331 \n",
       "L 187.961312 148.941992 \n",
       "L 188.57126 149.257249 \n",
       "L 189.181207 149.092943 \n",
       "L 189.791154 149.404391 \n",
       "L 190.401101 150.184669 \n",
       "L 191.011048 150.487832 \n",
       "L 191.620995 149.386156 \n",
       "L 192.84089 149.065728 \n",
       "L 193.450837 149.829103 \n",
       "L 194.060784 149.668303 \n",
       "L 194.670731 149.965354 \n",
       "L 195.280678 150.71384 \n",
       "L 195.890626 151.003257 \n",
       "L 196.500573 150.390008 \n",
       "L 197.720467 150.963861 \n",
       "L 198.330414 150.359186 \n",
       "L 198.940361 150.201818 \n",
       "L 199.550309 150.485703 \n",
       "L 200.160256 150.32919 \n",
       "L 200.770203 150.609961 \n",
       "L 201.990097 150.300005 \n",
       "L 202.600044 150.577169 \n",
       "L 203.819939 150.271587 \n",
       "L 204.429886 149.696344 \n",
       "L 205.039833 149.548709 \n",
       "L 205.64978 149.823121 \n",
       "L 206.259727 149.257249 \n",
       "L 206.869675 149.530561 \n",
       "L 207.479622 148.970771 \n",
       "L 208.089569 149.6566 \n",
       "L 208.699516 149.101025 \n",
       "L 209.309463 148.140002 \n",
       "L 209.91941 148.003868 \n",
       "L 211.139305 148.545002 \n",
       "L 211.749252 148.005562 \n",
       "L 212.359199 148.273892 \n",
       "L 212.969146 148.140002 \n",
       "L 213.579093 148.405579 \n",
       "L 214.189041 148.272255 \n",
       "L 214.798988 148.930245 \n",
       "L 215.408935 148.795878 \n",
       "L 216.018882 149.054517 \n",
       "L 216.628829 148.920729 \n",
       "L 217.238776 148.399206 \n",
       "L 217.848724 148.269097 \n",
       "L 218.458671 148.525724 \n",
       "L 221.508407 147.887866 \n",
       "L 222.728301 149.140784 \n",
       "L 223.338248 148.638466 \n",
       "L 223.948195 148.884838 \n",
       "L 224.558142 148.758321 \n",
       "L 225.16809 149.002361 \n",
       "L 225.778037 149.612728 \n",
       "L 226.387984 149.484907 \n",
       "L 226.997931 150.088873 \n",
       "L 227.607878 149.596187 \n",
       "L 228.217825 150.195228 \n",
       "L 228.827773 150.067147 \n",
       "L 230.047667 151.248499 \n",
       "L 231.267561 151.700441 \n",
       "L 232.487456 151.438919 \n",
       "L 233.097403 151.66174 \n",
       "L 234.317297 151.403318 \n",
       "L 234.927244 150.578719 \n",
       "L 235.537191 151.148575 \n",
       "L 236.147139 151.36847 \n",
       "L 236.757086 151.242141 \n",
       "L 237.97698 150.307609 \n",
       "L 239.196874 151.425319 \n",
       "L 239.806822 151.639652 \n",
       "L 241.026716 152.736549 \n",
       "L 241.636663 152.944147 \n",
       "L 242.24661 152.148255 \n",
       "L 242.856557 151.690694 \n",
       "L 243.466505 152.23148 \n",
       "L 244.076452 152.437963 \n",
       "L 244.686399 151.98408 \n",
       "L 245.296346 152.190013 \n",
       "L 245.906293 151.740011 \n",
       "L 246.51624 151.619201 \n",
       "L 247.736135 152.02801 \n",
       "L 248.346082 151.907446 \n",
       "L 248.956029 151.465831 \n",
       "L 249.565976 151.989512 \n",
       "L 250.785871 152.389181 \n",
       "L 252.615712 152.03221 \n",
       "L 253.225659 151.600198 \n",
       "L 254.445554 152.619751 \n",
       "L 255.055501 152.501547 \n",
       "L 255.665448 152.694633 \n",
       "L 256.275395 153.196052 \n",
       "L 256.885342 152.460007 \n",
       "L 257.495289 152.651398 \n",
       "L 259.935078 152.190013 \n",
       "L 260.545025 152.37926 \n",
       "L 261.154972 151.963614 \n",
       "L 261.76492 151.851465 \n",
       "L 262.374867 152.340008 \n",
       "L 263.594761 152.711782 \n",
       "L 264.204708 152.004227 \n",
       "L 264.814655 151.893671 \n",
       "L 265.424603 151.192895 \n",
       "L 266.644497 150.978678 \n",
       "L 267.254444 151.165304 \n",
       "L 267.864391 150.475144 \n",
       "L 268.474338 150.37115 \n",
       "L 269.084286 149.977621 \n",
       "L 269.694233 150.165 \n",
       "L 270.30418 150.062859 \n",
       "L 270.914127 150.248876 \n",
       "L 271.524074 150.720531 \n",
       "L 272.743969 151.085468 \n",
       "L 273.353916 150.982111 \n",
       "L 273.963863 151.162754 \n",
       "L 275.793704 152.541161 \n",
       "L 277.013599 152.329667 \n",
       "L 278.233493 153.231436 \n",
       "L 278.84344 152.847699 \n",
       "L 279.453387 153.018421 \n",
       "L 280.673282 152.80781 \n",
       "L 281.283229 152.429591 \n",
       "L 281.893176 152.872597 \n",
       "L 283.11307 153.20816 \n",
       "L 283.723018 153.6453 \n",
       "L 284.942912 152.896799 \n",
       "L 285.552859 152.794152 \n",
       "L 286.162806 152.959848 \n",
       "L 286.772753 152.857591 \n",
       "L 287.382701 152.489598 \n",
       "L 288.602595 152.289329 \n",
       "L 289.822489 152.618056 \n",
       "L 291.652331 153.888398 \n",
       "L 292.872225 153.684392 \n",
       "L 293.482172 152.805608 \n",
       "L 294.092119 152.190013 \n",
       "L 294.702067 152.093318 \n",
       "L 296.531908 152.573692 \n",
       "L 297.141855 152.477012 \n",
       "L 298.36175 152.792747 \n",
       "L 298.971697 153.202512 \n",
       "L 300.191591 153.512033 \n",
       "L 300.801538 153.414426 \n",
       "L 301.411485 153.066812 \n",
       "L 302.63138 153.373856 \n",
       "L 303.241327 153.277596 \n",
       "L 303.851274 153.677758 \n",
       "L 304.461221 153.581223 \n",
       "L 305.071168 153.731885 \n",
       "L 305.681116 153.635697 \n",
       "L 306.90101 153.934471 \n",
       "L 308.120904 153.743008 \n",
       "L 308.730851 154.134002 \n",
       "L 309.950746 153.942988 \n",
       "L 310.560693 153.365818 \n",
       "L 311.17064 153.513279 \n",
       "L 312.390534 154.284838 \n",
       "L 313.000482 154.428953 \n",
       "L 313.610429 154.81059 \n",
       "L 314.220376 154.477416 \n",
       "L 314.830323 154.382937 \n",
       "L 315.44027 154.052414 \n",
       "L 316.660165 154.808287 \n",
       "L 317.880059 154.62001 \n",
       "L 318.490006 154.059236 \n",
       "L 320.319848 154.48082 \n",
       "L 320.929795 154.851434 \n",
       "L 322.149689 154.666069 \n",
       "L 322.759636 154.80384 \n",
       "L 323.369583 153.79473 \n",
       "L 324.589478 154.072402 \n",
       "L 325.199425 153.755001 \n",
       "L 325.809372 153.893279 \n",
       "L 326.419319 153.804348 \n",
       "L 327.029266 154.167909 \n",
       "L 328.249161 153.990003 \n",
       "L 329.469055 153.365818 \n",
       "L 330.079002 153.27932 \n",
       "L 330.688949 153.639086 \n",
       "L 331.298897 153.774786 \n",
       "L 331.908844 153.244109 \n",
       "L 333.738685 152.988989 \n",
       "L 335.568527 154.050821 \n",
       "L 336.178474 153.746296 \n",
       "L 336.788421 153.225208 \n",
       "L 337.398368 152.923899 \n",
       "L 338.008315 152.840906 \n",
       "L 338.618263 152.10883 \n",
       "L 340.448104 152.51257 \n",
       "L 341.058051 152.216822 \n",
       "L 341.667998 151.708292 \n",
       "L 342.277946 152.056485 \n",
       "L 342.887893 151.976853 \n",
       "L 343.49784 151.684871 \n",
       "L 344.717734 151.951766 \n",
       "L 345.937629 151.794674 \n",
       "L 346.547576 152.137407 \n",
       "L 349.597312 152.788402 \n",
       "L 350.817206 152.21591 \n",
       "L 351.427153 152.345106 \n",
       "L 352.0371 152.680134 \n",
       "L 352.647048 152.80781 \n",
       "L 353.256995 152.318442 \n",
       "L 353.866942 152.446335 \n",
       "L 354.476889 152.164434 \n",
       "L 355.086836 152.087901 \n",
       "L 355.696783 152.215475 \n",
       "L 356.306731 152.545868 \n",
       "L 356.916678 152.469031 \n",
       "L 357.526625 152.595012 \n",
       "L 358.746519 152.442076 \n",
       "L 359.356466 152.567333 \n",
       "L 359.966414 152.491249 \n",
       "L 360.576361 151.814227 \n",
       "L 362.406202 151.592464 \n",
       "L 363.016149 151.121606 \n",
       "L 363.626097 151.247761 \n",
       "L 364.236044 151.571375 \n",
       "L 364.845991 151.103428 \n",
       "L 365.455938 151.031689 \n",
       "L 366.065885 150.76349 \n",
       "L 367.28578 150.622258 \n",
       "L 368.505674 150.87254 \n",
       "L 369.115621 150.607339 \n",
       "L 369.725568 150.732002 \n",
       "L 369.725568 150.732002 \n",
       "\" clip-path=\"url(#p5d83ec11e7)\" style=\"fill: none; stroke: #9467bd; stroke-width: 1.5; stroke-linecap: square\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_17\">\n",
       "    <path d=\"M 65.361932 115.740005 \n",
       "L 65.971879 164.340001 \n",
       "L 66.581826 148.140002 \n",
       "L 67.191773 140.04001 \n",
       "L 67.80172 135.18 \n",
       "L 68.411668 148.140002 \n",
       "L 69.021615 143.511431 \n",
       "L 69.631562 127.890008 \n",
       "L 70.241509 126.540004 \n",
       "L 70.851456 125.46001 \n",
       "L 71.461403 133.412729 \n",
       "L 72.071351 148.140002 \n",
       "L 73.291245 143.511431 \n",
       "L 73.901192 148.140002 \n",
       "L 74.511139 146.115004 \n",
       "L 75.121086 150.045884 \n",
       "L 75.731034 148.140002 \n",
       "L 76.340981 151.550533 \n",
       "L 77.560875 148.140002 \n",
       "L 78.170822 142.249099 \n",
       "L 78.780769 141.096526 \n",
       "L 79.390717 144.090006 \n",
       "L 80.000664 139.068008 \n",
       "L 80.610611 138.170772 \n",
       "L 81.220558 126.540004 \n",
       "L 81.830505 129.625718 \n",
       "L 82.440452 129.146908 \n",
       "L 83.0504 135.18 \n",
       "L 83.660347 134.552904 \n",
       "L 84.270294 127.890008 \n",
       "L 84.880241 130.467278 \n",
       "L 85.490188 127.175298 \n",
       "L 86.100135 126.848584 \n",
       "L 86.710083 121.140005 \n",
       "L 87.32003 126.24811 \n",
       "L 87.929977 128.529488 \n",
       "L 88.539924 120.72462 \n",
       "L 89.759819 125.222937 \n",
       "L 90.369766 124.997147 \n",
       "L 90.979713 127.042336 \n",
       "L 91.58966 131.203641 \n",
       "L 92.199607 130.86001 \n",
       "L 92.809554 134.757403 \n",
       "L 93.419502 132.284692 \n",
       "L 94.029449 135.990014 \n",
       "L 94.639396 133.593069 \n",
       "L 95.249343 133.236011 \n",
       "L 95.85929 134.798827 \n",
       "L 96.469237 138.170772 \n",
       "L 97.079185 137.747552 \n",
       "L 97.689132 133.740008 \n",
       "L 98.299079 135.18 \n",
       "L 98.909026 138.3043 \n",
       "L 99.518973 139.61369 \n",
       "L 100.12892 137.526208 \n",
       "L 100.738868 137.156955 \n",
       "L 101.348815 138.420012 \n",
       "L 101.958762 136.45476 \n",
       "L 102.568709 137.6884 \n",
       "L 103.178656 135.797146 \n",
       "L 104.398551 138.170772 \n",
       "L 105.008498 137.830921 \n",
       "L 105.618445 138.951948 \n",
       "L 106.228392 138.610591 \n",
       "L 106.838339 136.870449 \n",
       "L 107.448286 137.957149 \n",
       "L 109.278128 145.033156 \n",
       "L 109.888075 144.63731 \n",
       "L 111.107969 146.434737 \n",
       "L 111.717917 146.03611 \n",
       "L 112.327864 146.893848 \n",
       "L 113.547758 146.115004 \n",
       "L 114.157705 143.340014 \n",
       "L 114.767652 143.003422 \n",
       "L 115.3776 143.846024 \n",
       "L 116.597494 147.758829 \n",
       "L 118.427335 149.980909 \n",
       "L 119.64723 149.220011 \n",
       "L 120.257177 149.920222 \n",
       "L 121.477071 149.185162 \n",
       "L 122.087018 149.863416 \n",
       "L 122.696966 149.504214 \n",
       "L 123.91686 150.812171 \n",
       "L 124.526807 150.454288 \n",
       "L 125.136754 149.121824 \n",
       "L 125.746701 150.732002 \n",
       "L 127.576543 149.712826 \n",
       "L 128.18649 148.451551 \n",
       "L 128.796437 149.991439 \n",
       "L 130.016332 149.351221 \n",
       "L 130.626279 150.840009 \n",
       "L 131.236226 148.734509 \n",
       "L 131.846173 150.201818 \n",
       "L 133.066067 149.58644 \n",
       "L 133.676015 151.007269 \n",
       "L 134.895909 152.084352 \n",
       "L 135.505856 151.771036 \n",
       "L 136.115803 150.63231 \n",
       "L 136.72575 150.33662 \n",
       "L 137.335698 149.229078 \n",
       "L 137.945645 149.76 \n",
       "L 138.555592 147.872238 \n",
       "L 139.165539 147.608862 \n",
       "L 140.385433 145.527101 \n",
       "L 141.605328 145.054288 \n",
       "L 142.215275 143.292767 \n",
       "L 142.825222 142.318129 \n",
       "L 144.045116 143.404627 \n",
       "L 145.265011 141.512736 \n",
       "L 145.874958 142.780616 \n",
       "L 146.484905 141.853441 \n",
       "L 147.094852 143.100001 \n",
       "L 147.704799 142.184124 \n",
       "L 148.314747 142.700592 \n",
       "L 149.534641 140.914101 \n",
       "L 150.144588 141.428584 \n",
       "L 150.754535 141.246391 \n",
       "L 151.97443 139.530219 \n",
       "L 153.194324 140.542762 \n",
       "L 155.024165 140.04001 \n",
       "L 155.634113 140.529263 \n",
       "L 156.24406 141.660008 \n",
       "L 156.854007 140.844636 \n",
       "L 157.463954 139.40053 \n",
       "L 158.683848 140.355586 \n",
       "L 159.293796 138.942592 \n",
       "L 159.903743 138.170772 \n",
       "L 160.51369 135.55147 \n",
       "L 161.123637 135.426082 \n",
       "L 161.733584 136.52492 \n",
       "L 162.953479 136.266715 \n",
       "L 163.563426 135.540013 \n",
       "L 164.173373 136.014854 \n",
       "L 164.78332 135.891234 \n",
       "L 166.003214 136.819523 \n",
       "L 166.613162 136.693296 \n",
       "L 167.223109 137.725725 \n",
       "L 167.833056 137.020488 \n",
       "L 168.443003 137.467071 \n",
       "L 169.05295 138.476847 \n",
       "L 169.662897 138.344652 \n",
       "L 170.272845 137.652146 \n",
       "L 170.882792 138.084839 \n",
       "L 172.102686 136.726377 \n",
       "L 172.712633 136.607797 \n",
       "L 173.32258 137.58271 \n",
       "L 173.932528 136.917666 \n",
       "L 175.152422 137.757691 \n",
       "L 175.762369 137.636706 \n",
       "L 177.592211 138.857846 \n",
       "L 178.202158 138.73356 \n",
       "L 178.812105 139.130376 \n",
       "L 181.251894 136.604929 \n",
       "L 181.861841 137.508755 \n",
       "L 183.081735 136.282271 \n",
       "L 183.691682 135.18 \n",
       "L 184.301629 135.080829 \n",
       "L 184.911577 134.489247 \n",
       "L 185.521524 133.412729 \n",
       "L 186.741418 134.208013 \n",
       "L 187.351365 135.083291 \n",
       "L 188.57126 134.892712 \n",
       "L 189.181207 135.275305 \n",
       "L 189.791154 135.18 \n",
       "L 190.401101 134.613795 \n",
       "L 191.011048 134.992187 \n",
       "L 191.620995 135.834239 \n",
       "L 192.84089 135.642863 \n",
       "L 194.060784 136.372086 \n",
       "L 194.670731 136.275217 \n",
       "L 195.280678 136.633463 \n",
       "L 196.500573 136.440001 \n",
       "L 197.11052 137.24047 \n",
       "L 198.330414 137.044111 \n",
       "L 199.550309 137.730953 \n",
       "L 200.770203 137.533726 \n",
       "L 201.38015 137.002513 \n",
       "L 201.990097 135.612013 \n",
       "L 202.600044 135.954166 \n",
       "L 203.209992 135.865119 \n",
       "L 203.819939 136.62948 \n",
       "L 204.429886 136.962711 \n",
       "L 205.039833 136.870449 \n",
       "L 205.64978 135.937408 \n",
       "L 206.259727 135.431383 \n",
       "L 206.869675 135.764036 \n",
       "L 207.479622 135.678465 \n",
       "L 208.089569 135.18 \n",
       "L 209.309463 136.656463 \n",
       "L 211.139305 137.610012 \n",
       "L 211.749252 137.115937 \n",
       "L 212.359199 137.429268 \n",
       "L 212.969146 136.94 \n",
       "L 213.579093 136.056394 \n",
       "L 214.189041 136.370217 \n",
       "L 216.018882 136.120659 \n",
       "L 216.628829 136.429167 \n",
       "L 218.458671 136.182868 \n",
       "L 219.068618 136.486248 \n",
       "L 219.678565 137.169933 \n",
       "L 220.288512 135.942362 \n",
       "L 221.508407 137.297985 \n",
       "L 222.118354 136.837686 \n",
       "L 223.338248 137.423083 \n",
       "L 223.948195 136.967592 \n",
       "L 224.558142 136.886569 \n",
       "L 225.16809 136.436583 \n",
       "L 226.387984 137.01397 \n",
       "L 226.997931 136.93399 \n",
       "L 227.607878 137.218657 \n",
       "L 228.827773 137.058971 \n",
       "L 229.43772 137.700001 \n",
       "L 230.047667 137.260298 \n",
       "L 230.657614 136.10913 \n",
       "L 231.267561 136.034509 \n",
       "L 231.877508 135.605698 \n",
       "L 233.70735 136.44326 \n",
       "L 234.317297 135.669499 \n",
       "L 235.537191 136.915725 \n",
       "L 237.367033 136.691239 \n",
       "L 237.97698 137.301983 \n",
       "L 238.586927 136.885266 \n",
       "L 239.196874 137.151191 \n",
       "L 239.806822 136.060565 \n",
       "L 241.026716 135.919941 \n",
       "L 241.636663 136.520691 \n",
       "L 242.24661 136.783313 \n",
       "L 242.856557 136.378357 \n",
       "L 243.466505 136.307922 \n",
       "L 245.906293 137.340003 \n",
       "L 246.51624 137.919867 \n",
       "L 247.126188 138.170772 \n",
       "L 248.346082 139.313424 \n",
       "L 248.956029 139.23537 \n",
       "L 250.175923 140.359743 \n",
       "L 250.785871 140.279024 \n",
       "L 251.395818 140.516473 \n",
       "L 252.005765 140.435769 \n",
       "L 252.615712 140.986767 \n",
       "L 253.225659 140.905063 \n",
       "L 253.835606 140.196784 \n",
       "L 254.445554 139.805602 \n",
       "L 255.055501 139.728475 \n",
       "L 255.665448 139.030741 \n",
       "L 257.495289 137.886844 \n",
       "L 258.105237 137.203724 \n",
       "L 258.715184 137.747552 \n",
       "L 259.325131 137.983263 \n",
       "L 259.935078 137.913755 \n",
       "L 260.545025 137.54188 \n",
       "L 261.154972 137.776027 \n",
       "L 261.76492 137.707808 \n",
       "L 262.984814 136.974472 \n",
       "L 263.594761 137.20749 \n",
       "L 265.424603 137.011739 \n",
       "L 267.254444 137.697843 \n",
       "L 267.864391 138.215687 \n",
       "L 268.474338 138.439406 \n",
       "L 269.084286 138.081493 \n",
       "L 269.694233 138.015012 \n",
       "L 270.914127 137.308052 \n",
       "L 272.134021 137.181187 \n",
       "L 272.743969 137.6884 \n",
       "L 273.353916 137.340003 \n",
       "L 273.963863 137.56042 \n",
       "L 274.57381 137.214427 \n",
       "L 275.793704 137.0903 \n",
       "L 276.403652 137.588996 \n",
       "L 277.013599 137.805531 \n",
       "L 278.84344 139.278474 \n",
       "L 279.453387 139.487738 \n",
       "L 280.063335 139.145106 \n",
       "L 281.283229 139.560853 \n",
       "L 281.893176 139.493937 \n",
       "L 282.503123 139.699667 \n",
       "L 283.11307 139.632751 \n",
       "L 283.723018 139.295435 \n",
       "L 285.552859 139.905759 \n",
       "L 286.162806 139.571412 \n",
       "L 287.382701 139.440824 \n",
       "L 287.992648 139.110504 \n",
       "L 288.602595 139.576524 \n",
       "L 290.432436 139.383251 \n",
       "L 291.042384 139.843507 \n",
       "L 291.652331 139.51743 \n",
       "L 292.262278 139.714267 \n",
       "L 293.482172 139.586402 \n",
       "L 294.092119 140.04001 \n",
       "L 295.312014 140.425717 \n",
       "L 295.921961 140.873517 \n",
       "L 297.751802 141.439491 \n",
       "L 298.971697 140.799388 \n",
       "L 300.191591 140.66954 \n",
       "L 300.801538 141.107447 \n",
       "L 302.63138 140.16463 \n",
       "L 303.241327 140.102161 \n",
       "L 304.461221 140.472833 \n",
       "L 306.291063 140.285455 \n",
       "L 306.90101 139.978801 \n",
       "L 307.510957 140.406338 \n",
       "L 309.950746 140.160907 \n",
       "L 310.560693 140.341493 \n",
       "L 311.17064 140.04001 \n",
       "L 311.780587 140.220002 \n",
       "L 312.390534 139.680896 \n",
       "L 313.000482 139.622076 \n",
       "L 314.220376 139.980597 \n",
       "L 314.830323 140.395619 \n",
       "L 316.050217 140.275924 \n",
       "L 316.660165 140.451875 \n",
       "L 317.880059 140.332774 \n",
       "L 319.099953 140.681011 \n",
       "L 319.7099 140.621352 \n",
       "L 320.319848 140.793942 \n",
       "L 320.929795 140.734297 \n",
       "L 321.539742 140.444039 \n",
       "L 322.149689 140.615833 \n",
       "L 322.759636 140.327241 \n",
       "L 323.369583 140.727736 \n",
       "L 323.979531 140.440244 \n",
       "L 324.589478 140.838596 \n",
       "L 325.199425 140.324547 \n",
       "L 326.419319 141.116224 \n",
       "L 327.029266 141.057216 \n",
       "L 328.249161 141.390014 \n",
       "L 329.469055 142.167656 \n",
       "L 330.079002 142.10691 \n",
       "L 330.688949 142.492298 \n",
       "L 331.298897 142.431089 \n",
       "L 333.128738 142.911825 \n",
       "L 333.738685 142.629809 \n",
       "L 334.348632 142.788871 \n",
       "L 334.95858 142.727822 \n",
       "L 335.568527 142.229198 \n",
       "L 336.788421 142.110415 \n",
       "L 337.398368 142.268869 \n",
       "L 338.008315 141.99269 \n",
       "L 338.618263 142.150695 \n",
       "L 339.22821 142.092006 \n",
       "L 339.838157 142.249099 \n",
       "L 340.448104 141.975411 \n",
       "L 341.058051 142.132054 \n",
       "L 341.667998 142.07393 \n",
       "L 342.277946 141.802429 \n",
       "L 342.887893 141.745275 \n",
       "L 343.49784 141.901064 \n",
       "L 344.107787 141.84394 \n",
       "L 344.717734 141.998831 \n",
       "L 345.327681 141.94175 \n",
       "L 346.547576 142.249099 \n",
       "L 347.76747 141.715873 \n",
       "L 348.987365 142.021556 \n",
       "L 349.597312 142.381554 \n",
       "L 350.207259 142.324618 \n",
       "L 350.817206 142.475193 \n",
       "L 351.427153 142.4183 \n",
       "L 352.0371 141.948919 \n",
       "L 353.256995 142.249099 \n",
       "L 353.866942 141.988113 \n",
       "L 354.476889 141.932842 \n",
       "L 355.086836 142.286221 \n",
       "L 355.696783 142.026799 \n",
       "L 356.306731 141.56511 \n",
       "L 356.916678 141.71412 \n",
       "L 357.526625 141.457509 \n",
       "L 358.136572 141.606114 \n",
       "L 358.746519 141.95577 \n",
       "L 359.356466 142.102739 \n",
       "L 359.966414 142.449918 \n",
       "L 361.186308 142.34 \n",
       "L 361.796255 142.48497 \n",
       "L 363.016149 143.170682 \n",
       "L 363.626097 142.91633 \n",
       "L 365.455938 142.750967 \n",
       "L 366.065885 142.499526 \n",
       "L 366.675832 142.445457 \n",
       "L 367.28578 142.587588 \n",
       "L 368.505674 142.47977 \n",
       "L 369.115621 141.841811 \n",
       "L 369.725568 142.178403 \n",
       "L 369.725568 142.178403 \n",
       "\" clip-path=\"url(#p5d83ec11e7)\" style=\"fill: none; stroke: #8c564b; stroke-width: 1.5; stroke-linecap: square\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_18\">\n",
       "    <path d=\"M 50.14375 147.816007 \n",
       "L 384.94375 147.816007 \n",
       "\" clip-path=\"url(#p5d83ec11e7)\" style=\"fill: none; stroke-dasharray: 5.55,2.4; stroke-dashoffset: 0; stroke: #000000; stroke-width: 1.5\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 50.14375 256.68 \n",
       "L 50.14375 7.2 \n",
       "\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 384.94375 256.68 \n",
       "L 384.94375 7.2 \n",
       "\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 50.14375 256.68 \n",
       "L 384.94375 256.68 \n",
       "\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 50.14375 7.2 \n",
       "L 384.94375 7.2 \n",
       "\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n",
       "   </g>\n",
       "   <g id=\"legend_1\">\n",
       "    <g id=\"patch_7\">\n",
       "     <path d=\"M 302.089063 103.26875 \n",
       "L 377.94375 103.26875 \n",
       "Q 379.94375 103.26875 379.94375 101.26875 \n",
       "L 379.94375 14.2 \n",
       "Q 379.94375 12.2 377.94375 12.2 \n",
       "L 302.089063 12.2 \n",
       "Q 300.089063 12.2 300.089063 14.2 \n",
       "L 300.089063 101.26875 \n",
       "Q 300.089063 103.26875 302.089063 103.26875 \n",
       "z\n",
       "\" style=\"fill: #ffffff; opacity: 0.8; stroke: #cccccc; stroke-linejoin: miter\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_19\">\n",
       "     <path d=\"M 304.089063 20.298438 \n",
       "L 314.089063 20.298438 \n",
       "L 324.089063 20.298438 \n",
       "\" style=\"fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square\"/>\n",
       "    </g>\n",
       "    <g id=\"text_14\">\n",
       "     <!-- P(die=1) -->\n",
       "     <g transform=\"translate(332.089063 23.798438)scale(0.1 -0.1)\">\n",
       "      <defs>\n",
       "       <path id=\"DejaVuSans-50\" d=\"M 1259 4147 \n",
       "L 1259 2394 \n",
       "L 2053 2394 \n",
       "Q 2494 2394 2734 2622 \n",
       "Q 2975 2850 2975 3272 \n",
       "Q 2975 3691 2734 3919 \n",
       "Q 2494 4147 2053 4147 \n",
       "L 1259 4147 \n",
       "z\n",
       "M 628 4666 \n",
       "L 2053 4666 \n",
       "Q 2838 4666 3239 4311 \n",
       "Q 3641 3956 3641 3272 \n",
       "Q 3641 2581 3239 2228 \n",
       "Q 2838 1875 2053 1875 \n",
       "L 1259 1875 \n",
       "L 1259 0 \n",
       "L 628 0 \n",
       "L 628 4666 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-28\" d=\"M 1984 4856 \n",
       "Q 1566 4138 1362 3434 \n",
       "Q 1159 2731 1159 2009 \n",
       "Q 1159 1288 1364 580 \n",
       "Q 1569 -128 1984 -844 \n",
       "L 1484 -844 \n",
       "Q 1016 -109 783 600 \n",
       "Q 550 1309 550 2009 \n",
       "Q 550 2706 781 3412 \n",
       "Q 1013 4119 1484 4856 \n",
       "L 1984 4856 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-3d\" d=\"M 678 2906 \n",
       "L 4684 2906 \n",
       "L 4684 2381 \n",
       "L 678 2381 \n",
       "L 678 2906 \n",
       "z\n",
       "M 678 1631 \n",
       "L 4684 1631 \n",
       "L 4684 1100 \n",
       "L 678 1100 \n",
       "L 678 1631 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-29\" d=\"M 513 4856 \n",
       "L 1013 4856 \n",
       "Q 1481 4119 1714 3412 \n",
       "Q 1947 2706 1947 2009 \n",
       "Q 1947 1309 1714 600 \n",
       "Q 1481 -109 1013 -844 \n",
       "L 513 -844 \n",
       "Q 928 -128 1133 580 \n",
       "Q 1338 1288 1338 2009 \n",
       "Q 1338 2731 1133 3434 \n",
       "Q 928 4138 513 4856 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-28\" x=\"60.302734\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-64\" x=\"99.316406\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-69\" x=\"162.792969\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-65\" x=\"190.576172\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-3d\" x=\"252.099609\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-31\" x=\"335.888672\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-29\" x=\"399.511719\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_20\">\n",
       "     <path d=\"M 304.089063 34.976563 \n",
       "L 314.089063 34.976563 \n",
       "L 324.089063 34.976563 \n",
       "\" style=\"fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square\"/>\n",
       "    </g>\n",
       "    <g id=\"text_15\">\n",
       "     <!-- P(die=2) -->\n",
       "     <g transform=\"translate(332.089063 38.476563)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-28\" x=\"60.302734\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-64\" x=\"99.316406\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-69\" x=\"162.792969\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-65\" x=\"190.576172\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-3d\" x=\"252.099609\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-32\" x=\"335.888672\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-29\" x=\"399.511719\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_21\">\n",
       "     <path d=\"M 304.089063 49.654688 \n",
       "L 314.089063 49.654688 \n",
       "L 324.089063 49.654688 \n",
       "\" style=\"fill: none; stroke: #2ca02c; stroke-width: 1.5; stroke-linecap: square\"/>\n",
       "    </g>\n",
       "    <g id=\"text_16\">\n",
       "     <!-- P(die=3) -->\n",
       "     <g transform=\"translate(332.089063 53.154688)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-28\" x=\"60.302734\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-64\" x=\"99.316406\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-69\" x=\"162.792969\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-65\" x=\"190.576172\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-3d\" x=\"252.099609\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-33\" x=\"335.888672\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-29\" x=\"399.511719\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_22\">\n",
       "     <path d=\"M 304.089063 64.332813 \n",
       "L 314.089063 64.332813 \n",
       "L 324.089063 64.332813 \n",
       "\" style=\"fill: none; stroke: #d62728; stroke-width: 1.5; stroke-linecap: square\"/>\n",
       "    </g>\n",
       "    <g id=\"text_17\">\n",
       "     <!-- P(die=4) -->\n",
       "     <g transform=\"translate(332.089063 67.832813)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-28\" x=\"60.302734\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-64\" x=\"99.316406\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-69\" x=\"162.792969\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-65\" x=\"190.576172\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-3d\" x=\"252.099609\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-34\" x=\"335.888672\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-29\" x=\"399.511719\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_23\">\n",
       "     <path d=\"M 304.089063 79.010938 \n",
       "L 314.089063 79.010938 \n",
       "L 324.089063 79.010938 \n",
       "\" style=\"fill: none; stroke: #9467bd; stroke-width: 1.5; stroke-linecap: square\"/>\n",
       "    </g>\n",
       "    <g id=\"text_18\">\n",
       "     <!-- P(die=5) -->\n",
       "     <g transform=\"translate(332.089063 82.510938)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-28\" x=\"60.302734\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-64\" x=\"99.316406\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-69\" x=\"162.792969\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-65\" x=\"190.576172\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-3d\" x=\"252.099609\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-35\" x=\"335.888672\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-29\" x=\"399.511719\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_24\">\n",
       "     <path d=\"M 304.089063 93.689063 \n",
       "L 314.089063 93.689063 \n",
       "L 324.089063 93.689063 \n",
       "\" style=\"fill: none; stroke: #8c564b; stroke-width: 1.5; stroke-linecap: square\"/>\n",
       "    </g>\n",
       "    <g id=\"text_19\">\n",
       "     <!-- P(die=6) -->\n",
       "     <g transform=\"translate(332.089063 97.189063)scale(0.1 -0.1)\">\n",
       "      <defs>\n",
       "       <path id=\"DejaVuSans-36\" d=\"M 2113 2584 \n",
       "Q 1688 2584 1439 2293 \n",
       "Q 1191 2003 1191 1497 \n",
       "Q 1191 994 1439 701 \n",
       "Q 1688 409 2113 409 \n",
       "Q 2538 409 2786 701 \n",
       "Q 3034 994 3034 1497 \n",
       "Q 3034 2003 2786 2293 \n",
       "Q 2538 2584 2113 2584 \n",
       "z\n",
       "M 3366 4563 \n",
       "L 3366 3988 \n",
       "Q 3128 4100 2886 4159 \n",
       "Q 2644 4219 2406 4219 \n",
       "Q 1781 4219 1451 3797 \n",
       "Q 1122 3375 1075 2522 \n",
       "Q 1259 2794 1537 2939 \n",
       "Q 1816 3084 2150 3084 \n",
       "Q 2853 3084 3261 2657 \n",
       "Q 3669 2231 3669 1497 \n",
       "Q 3669 778 3244 343 \n",
       "Q 2819 -91 2113 -91 \n",
       "Q 1303 -91 875 529 \n",
       "Q 447 1150 447 2328 \n",
       "Q 447 3434 972 4092 \n",
       "Q 1497 4750 2381 4750 \n",
       "Q 2619 4750 2861 4703 \n",
       "Q 3103 4656 3366 4563 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-28\" x=\"60.302734\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-64\" x=\"99.316406\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-69\" x=\"162.792969\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-65\" x=\"190.576172\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-3d\" x=\"252.099609\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-36\" x=\"335.888672\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-29\" x=\"399.511719\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p5d83ec11e7\">\n",
       "   <rect x=\"50.14375\" y=\"7.2\" width=\"334.8\" height=\"249.48\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 600x450 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "counts = multinomial.Multinomial(10, fair_probs).sample((500,))\n",
    "cum_counts = counts.cumsum(dim=0)\n",
    "estimates = cum_counts / cum_counts.sum(dim=1, keepdims=True)\n",
    "\n",
    "d2l.set_figsize((6, 4.5))\n",
    "for i in range(6):\n",
    "    d2l.plt.plot(estimates[:, i].numpy(),\n",
    "                 label=(\"P(die=\" + str(i + 1) + \")\"))\n",
    "d2l.plt.axhline(y=0.167, color='black', linestyle='dashed')\n",
    "d2l.plt.gca().set_xlabel('Groups of experiments')\n",
    "d2l.plt.gca().set_ylabel('Estimated probability')\n",
    "d2l.plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6400f71",
   "metadata": {
    "origin_pos": 25
   },
   "source": [
    "每条实线对应于骰子的6个值中的一个，并给出骰子在每组实验后出现值的估计概率。\n",
    "当我们通过更多的实验获得更多的数据时，这$6$条实体曲线向真实概率收敛。\n",
    "\n",
    "### 概率论公理\n",
    "\n",
    "在处理骰子掷出时，我们将集合$\\mathcal{S} = \\{1, 2, 3, 4, 5, 6\\}$\n",
    "称为*样本空间*（sample space）或*结果空间*（outcome space），\n",
    "其中每个元素都是*结果*（outcome）。\n",
    "*事件*（event）是一组给定样本空间的随机结果。\n",
    "例如，“看到$5$”（$\\{5\\}$）和“看到奇数”（$\\{1, 3, 5\\}$）都是掷出骰子的有效事件。\n",
    "注意，如果一个随机实验的结果在$\\mathcal{A}$中，则事件$\\mathcal{A}$已经发生。\n",
    "也就是说，如果投掷出$3$点，因为$3 \\in \\{1, 3, 5\\}$，我们可以说，“看到奇数”的事件发生了。\n",
    "\n",
    "*概率*（probability）可以被认为是将集合映射到真实值的函数。\n",
    "在给定的样本空间$\\mathcal{S}$中，事件$\\mathcal{A}$的概率，\n",
    "表示为$P(\\mathcal{A})$，满足以下属性：\n",
    "\n",
    "* 对于任意事件$\\mathcal{A}$，其概率从不会是负数，即$P(\\mathcal{A}) \\geq 0$；\n",
    "* 整个样本空间的概率为$1$，即$P(\\mathcal{S}) = 1$；\n",
    "* 对于*互斥*（mutually exclusive）事件（对于所有$i \\neq j$都有$\\mathcal{A}_i \\cap \\mathcal{A}_j = \\emptyset$）的任意一个可数序列$\\mathcal{A}_1, \\mathcal{A}_2, \\ldots$，序列中任意一个事件发生的概率等于它们各自发生的概率之和，即$P(\\bigcup_{i=1}^{\\infty} \\mathcal{A}_i) = \\sum_{i=1}^{\\infty} P(\\mathcal{A}_i)$。\n",
    "\n",
    "以上也是概率论的公理，由科尔莫戈罗夫于1933年提出。\n",
    "有了这个公理系统，我们可以避免任何关于随机性的哲学争论；\n",
    "相反，我们可以用数学语言严格地推理。\n",
    "例如，假设事件$\\mathcal{A}_1$为整个样本空间，\n",
    "且当所有$i > 1$时的$\\mathcal{A}_i = \\emptyset$，\n",
    "那么我们可以证明$P(\\emptyset) = 0$，即不可能发生事件的概率是$0$。\n",
    "\n",
    "### 随机变量\n",
    "\n",
    "在我们掷骰子的随机实验中，我们引入了*随机变量*（random variable）的概念。\n",
    "随机变量几乎可以是任何数量，并且它可以在随机实验的一组可能性中取一个值。\n",
    "考虑一个随机变量$X$，其值在掷骰子的样本空间$\\mathcal{S}=\\{1,2,3,4,5,6\\}$中。\n",
    "我们可以将事件“看到一个$5$”表示为$\\{X=5\\}$或$X=5$，\n",
    "其概率表示为$P(\\{X=5\\})$或$P(X=5)$。\n",
    "通过$P(X=a)$，我们区分了随机变量$X$和$X$可以采取的值（例如$a$）。\n",
    "然而，这可能会导致繁琐的表示。\n",
    "为了简化符号，一方面，我们可以将$P(X)$表示为随机变量$X$上的*分布*（distribution）：\n",
    "分布告诉我们$X$获得某一值的概率。\n",
    "另一方面，我们可以简单用$P(a)$表示随机变量取值$a$的概率。\n",
    "由于概率论中的事件是来自样本空间的一组结果，因此我们可以为随机变量指定值的可取范围。\n",
    "例如，$P(1 \\leq X \\leq 3)$表示事件$\\{1 \\leq X \\leq 3\\}$，\n",
    "即$\\{X = 1, 2, \\text{or}, 3\\}$的概率。\n",
    "等价地，$P(1 \\leq X \\leq 3)$表示随机变量$X$从$\\{1, 2, 3\\}$中取值的概率。\n",
    "\n",
    "请注意，*离散*（discrete）随机变量（如骰子的每一面）\n",
    "和*连续*（continuous）随机变量（如人的体重和身高）之间存在微妙的区别。\n",
    "现实生活中，测量两个人是否具有完全相同的身高没有太大意义。\n",
    "如果我们进行足够精确的测量，最终会发现这个星球上没有两个人具有完全相同的身高。\n",
    "在这种情况下，询问某人的身高是否落入给定的区间，比如是否在1.79米和1.81米之间更有意义。\n",
    "在这些情况下，我们将这个看到某个数值的可能性量化为*密度*（density）。\n",
    "高度恰好为1.80米的概率为0，但密度不是0。\n",
    "在任何两个不同高度之间的区间，我们都有非零的概率。\n",
    "在本节的其余部分中，我们将考虑离散空间中的概率。\n",
    "连续随机变量的概率可以参考深度学习数学附录中[随机变量](https://d2l.ai/chapter_appendix-mathematics-for-deep-learning/random-variables.html)\n",
    "的一节。\n",
    "\n",
    "## 处理多个随机变量\n",
    "\n",
    "很多时候，我们会考虑多个随机变量。\n",
    "比如，我们可能需要对疾病和症状之间的关系进行建模。\n",
    "给定一个疾病和一个症状，比如“流感”和“咳嗽”，以某个概率存在或不存在于某个患者身上。\n",
    "我们需要估计这些概率以及概率之间的关系，以便我们可以运用我们的推断来实现更好的医疗服务。\n",
    "\n",
    "再举一个更复杂的例子：图像包含数百万像素，因此有数百万个随机变量。\n",
    "在许多情况下，图像会附带一个*标签*（label），标识图像中的对象。\n",
    "我们也可以将标签视为一个随机变量。\n",
    "我们甚至可以将所有元数据视为随机变量，例如位置、时间、光圈、焦距、ISO、对焦距离和相机类型。\n",
    "所有这些都是联合发生的随机变量。\n",
    "当我们处理多个随机变量时，会有若干个变量是我们感兴趣的。\n",
    "\n",
    "### 联合概率\n",
    "\n",
    "第一个被称为*联合概率*（joint probability）$P(A=a,B=b)$。\n",
    "给定任意值$a$和$b$，联合概率可以回答：$A=a$和$B=b$同时满足的概率是多少？\n",
    "请注意，对于任何$a$和$b$的取值，$P(A = a, B=b) \\leq P(A=a)$。\n",
    "这点是确定的，因为要同时发生$A=a$和$B=b$，$A=a$就必须发生，$B=b$也必须发生（反之亦然）。因此，$A=a$和$B=b$同时发生的可能性不大于$A=a$或是$B=b$单独发生的可能性。\n",
    "\n",
    "### 条件概率\n",
    "\n",
    "联合概率的不等式带给我们一个有趣的比率：\n",
    "$0 \\leq \\frac{P(A=a, B=b)}{P(A=a)} \\leq 1$。\n",
    "我们称这个比率为*条件概率*（conditional probability），\n",
    "并用$P(B=b \\mid A=a)$表示它：它是$B=b$的概率，前提是$A=a$已发生。\n",
    "\n",
    "### 贝叶斯定理\n",
    "\n",
    "使用条件概率的定义，我们可以得出统计学中最有用的方程之一：\n",
    "*Bayes定理*（Bayes' theorem）。\n",
    "根据*乘法法则*（multiplication rule ）可得到$P(A, B) = P(B \\mid A) P(A)$。\n",
    "根据对称性，可得到$P(A, B) = P(A \\mid B) P(B)$。\n",
    "假设$P(B)>0$，求解其中一个条件变量，我们得到\n",
    "\n",
    "$$P(A \\mid B) = \\frac{P(B \\mid A) P(A)}{P(B)}.$$\n",
    "\n",
    "请注意，这里我们使用紧凑的表示法：\n",
    "其中$P(A, B)$是一个*联合分布*（joint distribution），\n",
    "$P(A \\mid B)$是一个*条件分布*（conditional distribution）。\n",
    "这种分布可以在给定值$A = a, B=b$上进行求值。\n",
    "\n",
    "### 边际化\n",
    "\n",
    "为了能进行事件概率求和，我们需要*求和法则*（sum rule），\n",
    "即$B$的概率相当于计算$A$的所有可能选择，并将所有选择的联合概率聚合在一起：\n",
    "\n",
    "$$P(B) = \\sum_{A} P(A, B),$$\n",
    "\n",
    "这也称为*边际化*（marginalization）。\n",
    "边际化结果的概率或分布称为*边际概率*（marginal probability）\n",
    "或*边际分布*（marginal distribution）。\n",
    "\n",
    "### 独立性\n",
    "\n",
    "另一个有用属性是*依赖*（dependence）与*独立*（independence）。\n",
    "如果两个随机变量$A$和$B$是独立的，意味着事件$A$的发生跟$B$事件的发生无关。\n",
    "在这种情况下，统计学家通常将这一点表述为$A \\perp  B$。\n",
    "根据贝叶斯定理，马上就能同样得到$P(A \\mid B) = P(A)$。\n",
    "在所有其他情况下，我们称$A$和$B$依赖。\n",
    "比如，两次连续抛出一个骰子的事件是相互独立的。\n",
    "相比之下，灯开关的位置和房间的亮度并不是（因为可能存在灯泡坏掉、电源故障，或者开关故障）。\n",
    "\n",
    "由于$P(A \\mid B) = \\frac{P(A, B)}{P(B)} = P(A)$等价于$P(A, B) = P(A)P(B)$，\n",
    "因此两个随机变量是独立的，当且仅当两个随机变量的联合分布是其各自分布的乘积。\n",
    "同样地，给定另一个随机变量$C$时，两个随机变量$A$和$B$是*条件独立的*（conditionally independent），\n",
    "当且仅当$P(A, B \\mid C) = P(A \\mid C)P(B \\mid C)$。\n",
    "这个情况表示为$A \\perp B \\mid C$。\n",
    "\n",
    "### 应用\n",
    ":label:`subsec_probability_hiv_app`\n",
    "\n",
    "我们实战演练一下！\n",
    "假设一个医生对患者进行艾滋病病毒（HIV）测试。\n",
    "这个测试是相当准确的，如果患者健康但测试显示他患病，这个概率只有1%；\n",
    "如果患者真正感染HIV，它永远不会检测不出。\n",
    "我们使用$D_1$来表示诊断结果（如果阳性，则为$1$，如果阴性，则为$0$），\n",
    "$H$来表示感染艾滋病病毒的状态（如果阳性，则为$1$，如果阴性，则为$0$）。\n",
    "在 :numref:`conditional_prob_D1`中列出了这样的条件概率。\n",
    "\n",
    ":条件概率为$P(D_1 \\mid H)$\n",
    "\n",
    "| 条件概率 | $H=1$ | $H=0$ |\n",
    "|---|---|---|\n",
    "|$P(D_1 = 1 \\mid H)$|            1 |         0.01 |\n",
    "|$P(D_1 = 0 \\mid H)$|            0 |         0.99 |\n",
    ":label:`conditional_prob_D1`\n",
    "\n",
    "请注意，每列的加和都是1（但每行的加和不是），因为条件概率需要总和为1，就像概率一样。\n",
    "让我们计算如果测试出来呈阳性，患者感染HIV的概率，即$P(H = 1 \\mid D_1 = 1)$。\n",
    "显然，这将取决于疾病有多常见，因为它会影响错误警报的数量。\n",
    "假设人口总体是相当健康的，例如，$P(H=1) = 0.0015$。\n",
    "为了应用贝叶斯定理，我们需要运用边际化和乘法法则来确定\n",
    "\n",
    "$$\\begin{aligned}\n",
    "&P(D_1 = 1) \\\\\n",
    "=& P(D_1=1, H=0) + P(D_1=1, H=1)  \\\\\n",
    "=& P(D_1=1 \\mid H=0) P(H=0) + P(D_1=1 \\mid H=1) P(H=1) \\\\\n",
    "=& 0.011485.\n",
    "\\end{aligned}\n",
    "$$\n",
    "因此，我们得到\n",
    "\n",
    "$$\\begin{aligned}\n",
    "&P(H = 1 \\mid D_1 = 1)\\\\ =& \\frac{P(D_1=1 \\mid H=1) P(H=1)}{P(D_1=1)} \\\\ =& 0.1306 \\end{aligned}.$$\n",
    "\n",
    "换句话说，尽管使用了非常准确的测试，患者实际上患有艾滋病的几率只有13.06%。\n",
    "正如我们所看到的，概率可能是违反直觉的。\n",
    "\n",
    "患者在收到这样可怕的消息后应该怎么办？\n",
    "很可能，患者会要求医生进行另一次测试来确定病情。\n",
    "第二个测试具有不同的特性，它不如第一个测试那么精确，\n",
    "如 :numref:`conditional_prob_D2`所示。\n",
    "\n",
    ":条件概率为$P(D_2 \\mid H)$\n",
    "\n",
    "| 条件概率 | $H=1$ | $H=0$ |\n",
    "|---|---|---|\n",
    "|$P(D_2 = 1 \\mid H)$|            0.98 |         0.03 |\n",
    "|$P(D_2 = 0 \\mid H)$|            0.02 |         0.97 |\n",
    ":label:`conditional_prob_D2`\n",
    "\n",
    "不幸的是，第二次测试也显示阳性。让我们通过假设条件独立性来计算出应用Bayes定理的必要概率：\n",
    "\n",
    "$$\\begin{aligned}\n",
    "&P(D_1 = 1, D_2 = 1 \\mid H = 0) \\\\\n",
    "=& P(D_1 = 1 \\mid H = 0) P(D_2 = 1 \\mid H = 0)  \\\\\n",
    "=& 0.0003,\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "$$\\begin{aligned}\n",
    "&P(D_1 = 1, D_2 = 1 \\mid H = 1) \\\\\n",
    "=& P(D_1 = 1 \\mid H = 1) P(D_2 = 1 \\mid H = 1)  \\\\\n",
    "=& 0.98.\n",
    "\\end{aligned}\n",
    "$$\n",
    "现在我们可以应用边际化和乘法规则：\n",
    "\n",
    "$$\\begin{aligned}\n",
    "&P(D_1 = 1, D_2 = 1) \\\\\n",
    "=& P(D_1 = 1, D_2 = 1, H = 0) + P(D_1 = 1, D_2 = 1, H = 1)  \\\\\n",
    "=& P(D_1 = 1, D_2 = 1 \\mid H = 0)P(H=0) + P(D_1 = 1, D_2 = 1 \\mid H = 1)P(H=1)\\\\\n",
    "=& 0.00176955.\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "最后，鉴于存在两次阳性检测，患者患有艾滋病的概率为\n",
    "\n",
    "$$\\begin{aligned}\n",
    "&P(H = 1 \\mid D_1 = 1, D_2 = 1)\\\\\n",
    "=& \\frac{P(D_1 = 1, D_2 = 1 \\mid H=1) P(H=1)}{P(D_1 = 1, D_2 = 1)} \\\\\n",
    "=& 0.8307.\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "也就是说，第二次测试使我们能够对患病的情况获得更高的信心。\n",
    "尽管第二次检验比第一次检验的准确性要低得多，但它仍然显著提高我们的预测概率。\n",
    "\n",
    "## 期望和方差\n",
    "\n",
    "为了概括概率分布的关键特征，我们需要一些测量方法。\n",
    "一个随机变量$X$的*期望*（expectation，或平均值（average））表示为\n",
    "\n",
    "$$E[X] = \\sum_{x} x P(X = x).$$\n",
    "\n",
    "当函数$f(x)$的输入是从分布$P$中抽取的随机变量时，$f(x)$的期望值为\n",
    "\n",
    "$$E_{x \\sim P}[f(x)] = \\sum_x f(x) P(x).$$\n",
    "\n",
    "在许多情况下，我们希望衡量随机变量$X$与其期望值的偏置。这可以通过方差来量化\n",
    "\n",
    "$$\\mathrm{Var}[X] = E\\left[(X - E[X])^2\\right] =\n",
    "E[X^2] - E[X]^2.$$\n",
    "\n",
    "方差的平方根被称为*标准差*（standard deviation）。\n",
    "随机变量函数的方差衡量的是：当从该随机变量分布中采样不同值$x$时，\n",
    "函数值偏离该函数的期望的程度：\n",
    "\n",
    "$$\\mathrm{Var}[f(x)] = E\\left[\\left(f(x) - E[f(x)]\\right)^2\\right].$$\n",
    "\n",
    "## 小结\n",
    "\n",
    "* 我们可以从概率分布中采样。\n",
    "* 我们可以使用联合分布、条件分布、Bayes定理、边缘化和独立性假设来分析多个随机变量。\n",
    "* 期望和方差为概率分布的关键特征的概括提供了实用的度量形式。\n",
    "\n",
    "## 练习\n",
    "\n",
    "1. 进行$m=500$组实验，每组抽取$n=10$个样本。改变$m$和$n$，观察和分析实验结果。\n",
    "2. 给定两个概率为$P(\\mathcal{A})$和$P(\\mathcal{B})$的事件，计算$P(\\mathcal{A} \\cup \\mathcal{B})$和$P(\\mathcal{A} \\cap \\mathcal{B})$的上限和下限。（提示：使用[友元图](https://en.wikipedia.org/wiki/Venn_diagram)来展示这些情况。)\n",
    "3. 假设我们有一系列随机变量，例如$A$、$B$和$C$，其中$B$只依赖于$A$，而$C$只依赖于$B$，能简化联合概率$P(A, B, C)$吗？（提示：这是一个[马尔可夫链](https://en.wikipedia.org/wiki/Markov_chain)。)\n",
    "4. 在 :numref:`subsec_probability_hiv_app`中，第一个测试更准确。为什么不运行第一个测试两次，而是同时运行第一个和第二个测试?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98e5c674",
   "metadata": {
    "origin_pos": 27,
    "tab": [
     "pytorch"
    ]
   },
   "source": [
    "[Discussions](https://discuss.d2l.ai/t/1762)\n"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "name": "python"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}